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.
Jewell said afterwards: "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."
Eriksson insisted: "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."