City were forced to settle for a point against struggling Derby despite Daniel Sturridge's goal on his full debut.
Derby stunned City by taking the lead right after the half-time break
Darius Vassell twice missed when clean through as Derby began like a team that had lost its last five league games.
The Rams improved towards the break and Rob Earnshaw's shot hit the post before Sun Jihai deflected Kenny Miller's shot in for an own goal in the 47th minute.
Sturridge converted Martin Petrov's cross to level but neither team could fashion a winner despite late pressure.
Paul Jewell will be the happier of the two managers after a much more encouraging display from the hosts, although they have yet to win after 10 games under him.
He and opposite number Sven-Goran Eriksson wielded the axe following dismal FA Cup defeats at the weekend, the most high-profile of eight casualties being City's Brazilian playmaker Elano.
But while the visitors' standards have dipped in recent weeks, it was clear early on why Derby - watched by new owner Andy Appleby - are hurtling towards the Championship.
Vassell fired woefully wide after seizing on a terrible Claude Davis backpass and Vedran Corluka headed over when he was left all alone at a corner.
Another gilt-edged opportunity saw Vassell hesitate when Petrov played a brilliant first-time ball across the penalty area to allow Lewis Price time to smother his attempt.
It was desperate stuff from the Rams but all the chances were falling for the profligate Vassell.
He headed over yet another tremendous cross from Petrov and then got his legs in a tangle after bringing down a ball over the top.
Earnshaw almost showed him how to do it when he brilliantly turned following a pass from Miller and fired his shot against Joe Hart's left-hand post.
However, only a brave block from Davis kept Derby level shortly before the interval, when he got in the way of Stephen Ireland's fierce strike from six yards which was destined for the bottom left corner.
If City had gone off frustrated, they were beside themselves at the start of the second half when Miller's tame effort, which was going well wide, took a deflection off Sun and went to the left of a standed Hart.
Eriksson's men were shell-shocked for a while and the Swede introduced Elano in a bid to revive them.
Petrov continued to be the main creative source and his wonderful cross was met by Sturridge to make it 1-1 - and two goals in two games for the youngster - before another fine centre was volleyed over by that man Vassell.
There was plenty of attacking intent from both teams in the last 15 minutes but neither could manufacture a clear chance and a draw was probably a fair outcome.
Derby boss Paul Jewell:
"We fought like tigers. We're never going to be the best team in the world but people will put up with anything as long as they see you giving effort and no player can be questioned about his effort.
"As a group on Saturday it wasn't acceptable but at least we bounced back and showed a bit of moral courage.
"Getting a point against a team going for the Champions League is a start. I want to play a lot more football but the situation we're in we're playing for pride and if every player gives their all I can ask for no more."
Man City boss Sven-Goran Eriksson:
"In the first half alone we created three or four very good chances from which we should have scored and the goal they scored was not even a goalscoring chance.
"But if I compare what I saw last Sunday, when the attitude was not 100% right and we didn't fight or help each other, with this I can't complain.
"Hopefully we can keep playing like this and score more goals. With better skill from our side we would have scored more goals but we are working on it on and off the pitch."
Derby: Price, Leacock, Moore, Davis (Todd 69), Edworthy, Fagan, Savage, Ghaly, Pearson (Barnes 83), Earnshaw (Villa 88), Miller.
Subs Not Used: Hinchliffe, Robert.
Goals: Jihai 47 og.
Man City: Hart, Jihai, Dunne, Corluka, Ball, Etuhu (Elano 55), Ireland, Gelson, Petrov, Vassell (Mpenza 79), Sturridge (Geovanni 72).
Subs Not Used: Schmeichel, Hamann.
Goals: Sturridge 63.
Ref: Steve Bennett (Kent).
BBC Sport Player Rater man of the match: Man City's Martin Petrov 7.49 (on 90 minutes). Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.