Some Rangers fans have criticised the manager after a photograph emerged of McCoist apparently singing karaoke at a post-match function following their extra-time loss to Raith Rovers on Sunday.
Rangers appeared keen to avoid the issue as they previewed their William Hill Scottish Cup semi-final against Dundee United and McCoist delivered a terse response to a question on the incident before immediately exiting his media conference.
McCoist said: "What I will say to you is this. If you or anyone else in this room for one minute doesn't think myself or my staff were really, really hurting and in a lot of pain after a result which we should have won, then you are very, very wrong. I can assure you that. Thank you."
Rangers striker Jon Daly, like captain Lee McCulloch earlier this week, also side-stepped a question on the topic during the media preview.
But McCoist insisted he was as low as after any other game - although he maintained the League One champions' season could still be regarded a success despite cup defeats to Raith and Forfar.
"It was certainly as low as some of the things that have happened to us in the past in terms of football results," McCoist said.
"You tend to remember the defeats more than the victories. Thankfully we have had a lot more victories than defeats, but every defeat hurts."
The criticism over his coaching ability has also stung McCoist but he is determined to respond.
McCoist, who displayed a serious demeanour throughout his media duties, said: "I'm handling it fine because it does go with the territory. Listen, it's not nice, I wouldn't sit here for a minute and say it's pleasant, but it goes with the territory.
"If you can't stand it then you shouldn't be in the seat in the first place. There will be times in any manager's career when he receives criticism, not only from outside the football club but certainly from some of his own fans, who are well entitled to voice their opinions.
"I am absolutely no different to that. Our supporters don't need to be reassured, but if one or two of them did, they can be 100 per cent safe in the knowledge that we are hell-bent on getting the club back to the top.
"There will be one or two bumps along the way, we have always said that, but we just have to ride those bumps and keep going."
While the 1-0 defeat at Easter Road was one of those setbacks, McCoist does not believe lack of success in the cups so far has undermined their season.
"I actually consider the season a success now, in respect we have done the job that was 100 per cent required to do," the 51-year-old said.
"We won the league at a very, very early stage and that was the number one target. It would be an even bigger success if we could get to the Scottish Cup final and win it.
"Our target, in my opinion, is to get out of the division we are in. Anything else is a bonus. But don't get me wrong, we are looking for bonuses."
With Rangers struggling to entertain fans in recent weeks, United have been installed as clear favourites by the bookmakers for the Ibrox semi-final. While McCoist accepts they will have to raise their game, he is convinced they have the means to do so.
"We have 100 per cent faith in the plan and the way we'll play," McCoist said. "It's part of the job being a manager, you get criticism when things don't go well.
"I totally accept that and fully appreciate that, but we have not lost any belief in the way that we will have to perform, and can perform, to get a result.
"United are a good, good side, they have some real talent and pace middle to front and good experience at the back. We will definitely have to step up our level of performance, but we can do it.
"As down as we were last week, it's only the second game we have lost this season, both in extra-time, so we are looking forward rather than back."
Meanwhile, Dundee United midfielder Paul Paton is determined to enjoy the biggest game of his career to help banish his disappointment at missing out on Partick Thistle's title run-in.
The midfielder suffered a knee injury on March 27 last season that ruled him out for the rest of the campaign, forcing him to watch from the stands as his team-mates secured the First Division championship.
So he is eager to be in the thick of the action when United face Rangers at Ibrox in the William Hill Scottish Cup semi-finals.
Paton, whose move to Tannadice was agreed by the time of his injury, said: "That was a big blow in my career. I had a great time at Thistle and to get injured was a massive anti-climax because I didn't really feel part of things.
"So it makes me more determined to do well on Saturday.
"I think maybe people thought because I had a move I wasn't caring but I would have given anything to be on the park for those last games, especially the Morton game at home. It was a massive disappointment for me."
Paton sat out the win at Falkirk that clinched the title but still lifted the trophy after the final home game with player-manager Alan Archibald, who stepped up when Jackie McNamara left to become United boss.
But looking back, Paton said: "I was a bit embarrassed. I did play 25 league games but I still felt that Archie was our leader and should be the captain.
"To lift it with him was an honour but there was still part of me that was so disappointed I didn't play more games."
Playing against Rangers could help wipe away those blues, but Paton said: "It will only be a good occasion if I go and win. I will reflect after the game whether it's been successful or not.
"As a player you don't get too carried away. Although it's the biggest game I've played in, I'm 26 years old, I'm not a kid.
"I'll take it in my stride. That's why I came here, for big occasions like this.
"It would mean the world to get to a final. I always said I would look back at the end of the season and reflect, and getting to a final would be an achievement in itself."
The game has intrigued most of Scottish football as the League One champions face their first Premiership opposition of the season, and in the midst of a backlash following their Ramsdens Cup final defeat by Raith Rovers.
Rangers captain Lee McCulloch claimed United were favourites but Paton is trying to ignore the hype.
"I've not read many papers to see who is favourite or what's been said," he said. "Obviously Rangers had their disappointing result, but they are a massive club.
"They are going to have the majority of fans at their home pitch. If anyone is favourites, you would say it is them, but we will just go there confident in our work.
"We don't want to talk about Rangers, we just concentrate on Dundee United. If we play to our ability we do well, and we hope to do that on Saturday."
The former Queen's Park player, who has played at all 41 league grounds in Scotland other than Ibrox, added: "We only know how to play one way. If we get involved in battles, I don't think it suits us.
"We have some really talented boys and I have great faith in them that they can go and turn on the style."
Paton is among the most experienced players in the United team but he has no concerns over the prospect of young players such as 18-year-old Ryan Gauld suffering from nerves.
"The gaffer is a laid-back guy and all the players are laid-back too," he said.
"The young boys are the most laid-back out of anybody. If you get to know Gauldy, Mackay-Steven, Armstrong, Ciftci, any further laid back and they would be falling asleep. These guys are so chilled.
"It's water off a duck's back to these guys, it's a great attitude to have."