Stoke had been much the better side in the first half and should have taken the lead when Mame Biram Diouf scuffed an early effort, but they held on bravely as City upped the pressure towards the end.
The result left City third on 56 points, behind second-placed Tottenham Hotspur on goal difference, having failed to claw back any significant ground on Antonio Conte's table-toppers. Stoke remain ninth on 36 points.
"Frustrated is a tough word," City boss Pep Guardiola told Sky Sports. "We didn't win but we didn't lose. We created a lot of chances and they didn't. We tried. We made everything and fought like never before."
With fixtures coming thick and fast as City continue to fight on three fronts, Guardiola had tinkered with his team, dropping defender John Stones, playmaker Silva and forward Raheem Sterling.
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If he was hoping to inject fresh legs and added impetus, however, he would have been sorely disappointed with their first-half display as a sluggish City failed to create a single clear chance.
Stoke, who had scored just one and conceded 19 in their eight previous Premier League visits to the Etihad, began with purpose and should have taken the lead when Diouf made a poor connection with an effort that was easily saved after six minutes.
It took until the second half for City to crank into gear as Guardiola summoned Silva off the bench to generate some momentum.
They came close to breaking the deadlock when Sane lashed an effort over the bar after 60 minutes and then Silva pulled an one wide when bearing down on goal.
Silva had another shot from outside the box deflected wide before Nicolas Otamendi's header landed on the roof of the net, but City's best chance arrived in stoppage time when Iheanacho could only steer Kevin De Bruyne's excellent cross wide.
(Reporting by Toby Davis, editing by Pritha Sarkar)
