Criticism of McCoist's cup record was accompanied by anger from some fans after photographs emerged which appeared to show him singing karaoke at Ibrox after the game on Sunday.
The club confirmed a post-match function had taken place but questions on the issue went unanswered when captain Lee McCulloch met the media on Wednesday.
And McCoist only addressed the topic indirectly during an interview on the club's official website.
"I can assure everybody the players were feeling it along with the staff and all the supporters," he said.
"It has never been any different at this club. You win and lose together as a team and a squad and everybody feels the same.
"We were extremely low after Sunday but it is our job to get everybody back up and focused again."
McCoist and his players have the chance to redeem themselves when they play Dundee United at Ibrox in the William Hill Scottish Cup semi-finals on Saturday.
The club's record goalscorer said: "Rangers teams of the past have lost big, big games and they've always bounced back and showed a great mental attitude to do that. This team will hopefully be the same.
"We've seen and we can tell the players are well up for it and they're really motivated and focused on getting the job done.
"We're still really disappointed as you'd expect but we can't sit back and feel sorry for ourselves.
"There's absolutely no doubt we can move on. It's a game against a team which will definitely be favourites against us and they've had some good performances this season.
"Outwith their 2-0 defeat to Celtic last week, Dundee United have been scoring goals for fun and they've got some very good players from the middle to front.
"At the same time, our lads know what is expected of them and the game is getting played at our stadium.
"We'll have a fantastic support there and in an ideal world we'll give them something to shout about."
Winger Calum Gallagher potentially has two semi-finals to look forward to this weekend with Rangers taking on St Mirren in the SFA Youth Cup on Sunday.
The 19-year-old has now made four-first team appearances since making a goalscoring debut against Dunfermline last month.
He said: "It has been a bit crazy in the last few weeks and it has been brilliant to be involved in some of the games I've played in.
"I feel like I've really been accepted into the first team and it has been a massive life experience for me.
"I'm dead eager to push on but I'm not sure what this weekend has in store for me. There's a decision there to be made by the youth department and the first-team staff.
"I'm not sure if it's a big decision for them but it's a big one for me anyway and to play for the first team in a Scottish Cup semi-final would be amazing.
"By the same token, I've played in every round of the SFA Youth Cup and I want to see out this season with them as well.
"If I can do both I'd love to because I still see myself as an under-20 player and I think it's important for the team that I'm involved in that game to keep my feet on the ground."