Nicky Law will still be in charge against Wimbledon.
Speculation has been reaching fever pitch over the future of the City manager.
Saturday's last-gasp loss to Nottingham Forest was the sixth at home this season - the worst record in the country - and keeps City stuck in the relegation zone.
Chairman Gordon Gibb, who insisted before the game that a result was "paramount", has indicated that he will not make a change ahead of Saturday's TV clash away to the bottom club.
Gibb, who will spend the whole week at the ground, said: "Putting pressure on a manager is not in the best interests of the club and it's definitely not my job to do that at this stage.
"You'll get a tough, robust position from anyone at the club over the next week because that performance was good.
"I know fans don't like to focus on financial realities but we are out-performing this market in that we're competing on a level playing field. I'll argue with anyone that says we're not.
"We've put in some excellent performances this year. Obviously results are important but in terms of a financial building block we've put that squad together on very realistic parameters.
"The financial situation is still the most important issue facing this club.
"Stayaway fans and the negative mentality are putting a question mark against the club's sustainability and that's regrettable."
A few angry supporters behind the dug-out displayed "Law Out" banners after Forest netted the stoppage-time winner - but came under abuse from fans around them.
Gibb added: "It was a pretty good indication of the mood of the silent majority that the individuals concerned were told to put the banners away.
"The people in question had written that before they even saw how we played. If we'd won 8-0 would they have taken the banners home and come back with them another day?
"It seems some people have made up their minds and whatever I say isn't going to change that."
Law said: "At the end it was pleasing not to hear us get booed off. They could have quite easily done that but they were very supportive."
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article