The Light Blues forced their William Hill Scottish Cup tie to a replay with a controversial leveller after the Coatbridge men took a shock lead at Ibrox.
Fans vented their frustration as jeers rang around the stadium at the full-time whistle following Sunday's clash.
And some supporters took to social media to question whether McCoist is still the right man to lead the club forward - even though Rangers are potentially one game from wrapping up the League One title.
Asked if he has concerns over his job if Rangers fail to book a last-four meeting against Dundee United, McCoist said: "No, I don't. I've got an awful lot to worry about in terms of getting teams prepared for games.
"So I think I've got enough to worry about without starting to worry about other things.
"I don't give it enough thought to think whether [the criticism] is justified or over the top or not.
"The Rangers manager is guaranteed one thing and that's a level of criticism that comes his way. I 100 per cent expect and accept it.
"I will continue no matter what happens or what's said or written.
"I will continue in our quest to get the team back to where we belong and, in doing that, hopefully playing some good attractive football."
Rangers could take another step towards a return to the top level by clinching the championship when they host Airdrie on Wednesday night.
And McCoist is determined to guide his side over the line in style, acknowledging that fans should be able to expect entertainment as well as results.
He said: "We want to play well and we want to win it by entertaining and scoring goals. It's very important how we win it.
"The most important thing is winning - but it's important, if we can, to win it in style.
"The fans are entitled to their views and opinions. That hasn't changed over 140 years.
"We have looked back at the game and spoken about it and we can - and will - do better.
"I've been saying for 30-odd years that Rangers fans expect to win games and expect to be entertained along the way.
"That hasn't changed - it never will and nor should it."
One of the major talking points after the 1-1 draw with the Wee Rovers was whether Bilel Mohsni's equaliser should have been allowed to stand amid suggestions goalkeeper Neil Parry was fouled.
Asked for his own thoughts, Rangers number one Cammy Bell said: "The referee didn't give a foul so in his eyes it isn't a foul. Sometimes you get them, sometimes you don't.
"As a goalkeeper, I've been on both ends of it. The referee is there to make a decision and he has made it. I think you just need to get on with it.
"I think I would have done things differently as a goalkeeper to be honest.
"You've got to protect yourself. You've got the licence to bring your leg up and protect yourself.
"It's a contact sport. You're going to get a little nudge and it depends how much the referee sees it as being a foul or not.
"He didn't see it as a foul - it was a goal and one that we gratefully accepted."