City needed a 70th-minute strike from Yaya Toure to break the resistance of the spirited Potters at the Etihad Stadium and claim three valuable Barclays Premier League points.
It was a hard-fought 1-0 victory but it would have been more convincing had Edin Dzeko not missed embarrassingly from two yards.
Just moments after Toure's strike, the unmarked Bosnian was presented with an open goal but contrived to fluff his shot.
With Alvaro Negredo still to regain top form after recent injury, Stevan Jovetic coming on as a substitute and then going off again, and Sergio Aguero out, City's prolific forward line has temporarily seized up.
Pellegrini said: "I think it is normal during the season that sometimes the strikers may lose (the chances) to score but I trust in all of them. I am sure they will recover their normal performance.
"We didn't create many chances because Stoke defended very well.
"All the team were behind the ball and near the box, but we had the patience for the 90 minutes and finally we scored."
Pellegrini said he had not lost any faith in Dzeko - who has still scored 17 goals this season - after his remarkable miss.
He said: "Every player can have a bad day. Maybe he had a bad day, maybe he was nervous after he failed that goal but I will continue trusting in him."
City's victory was a welcome one in title terms, coming after rivals Chelsea had won earlier in the day.
It was the response required after failure to win on their last two Premier League outings, as well as the midweek Champions League loss to Barcelona.
Pellegrini has spoken often of his desire to win in style but on this occasion he was simply happy with the points.
He said: "The satisfaction is the same. We cannot expect to win by three or four goals every match. It is important to know how to win both ways."
Pellegrini said Jovetic, who came on just before the hour, was forced off with cramp, while Aguero, after five games out with hamstring trouble, will return to training next week.
Stoke boss Mark Hughes felt his side acquitted themselves well but paid a heavy price for some errors.
Hughes, formerly manager at Eastlands, said: "I was pleased with what we produced.
"We had a game plan and whenever you have one, you have to execute it to the best of your ability and I thought we did that for most of the game.
"We made a couple of errors that led to the goal and consecutive errors tend to lead to goals. Apart from that we were resolute.
"We had a couple of efforts where we might have scored, most notably Charlie's (Adam) effort where Joe Hart made an outstanding save."
Hughes was not happy with all of City's tactics, feeling that some of the home players pushed the boundaries of legality.
Vincent Kompany - a player Hughes signed for City - was one player Hughes commented about.
He said: "I thought on a couple of occasions - call it professionalism or good play, or a bit of cynical play - we had good opportunities that were stopped because my players were being taken out.
"The player that you mentioned and on three or four other occasions Stoke players were taken out quite cynically in my view.
"It is part of the game and the ref, in fairness, booked the majority of them but maybe he should have looked to give another yellow card."