Rangers are looking for their first Scottish Championship points of the season at Falkirk on Friday night after beginning the campaign with home defeat by Hearts.
That followed an unconvincing extra-time win over 10-man Hibernian in the Petrofac Training Cup and sparked some serious criticism of the Rangers boss.
McCoist did not seem like a man under pressure as he previewed the Falkirk trip and stated that the demise of the Edinburgh clubs had been exaggerated.
But he knows his team need to produce more consistent performances to kick-start their title challenge.
"Fans are entitled to their opinion," McCoist said. "Our fans have been fantastic so it would be completely wrong of me to ask them not to have an opinion.
"They have got an opinion and long may they continue voicing that opinion.
"There are far greater managers that have sat in this chair than me who have received stick after a poor result.
"If you look back and Walter Smith and Willie Waddell can get stick, then I don't think anyone is immune from that, and rightly so.
"We are all big boys and we know that criticism is part and parcel of football, none more so at this club. It's the way it's been for over 140 years and it's the way it will hopefully be for the next 140. We can all handle it fine.
"I've played here long enough and been involved in defeats, and the fear of defeat keeps you going more than anything. A lot of the boys have been here before or been here for a while now, and they do understand the pressure of having to win games at our club."
McCoist did not think his team would struggle to click as they step up another level, but he knew that their first two games would present a challenge.
The former Scotland striker said: "We have always said it would be a tough league, nobody I've spoken to thinks it's going to be a stroll in the park. Clearly it's not, it's going to be a tough and interesting league.
"I think there was perhaps a bit too much made of Hearts' and Hibs' demise.
"Obviously they are in a position they don't t want to be in. But I felt for the last three or four months of the season, Hearts were on the up. Hibs was a massive shock, but at the same time I was of the opinion that they were on the up again with a fine man coming in to take over and give everyone a lift (Alan Stubbs).
"So I didn't think Hearts and Hibs were as low as other people did. We are fine, there will be hiccups along the way in this league."
Striker Kenny Miller argued that the service had to improve following the 2-1 loss to Hearts.
"I used to say that myself when I was a striker," McCoist said. "I know where he's coming from, but in pre-season and the last couple of games we have missed some clear-cut chances."
McCoist added: "I would like us to be more consistent throughout the 90 minutes, I think we have played well in patches in the first two games."
While stressing that the Edinburgh clubs will pose a challenge, McCoist did not underestimate the threat posed by Falkirk among others.
New boss Peter Houston bolstered his squad with likes of former Hearts goalkeeper Jamie MacDonald in the summer, although they started their season with a 2-2 draw against Cowdenbeath.
McCoist said: "Peter's had a great managerial track record and you have younger managers at Dumbarton and Raith Rovers and Queen of the South in particular who are aiming to do very, very well.
"I can assure you, we aren't looking solely at Hearts and Hibs. I can absolutely assure everyone there will be points dropped throughout the season against clubs of quality like Dumbarton, Falkirk, Raith Rovers and Queen of the South and teams like that."