Pellegrini had made three changes to the side which lost 1-0 at home to Chelsea as they looked to take full advantage of Arsenal's 5-1 defeat at Liverpool.
However, it was the relegation-threatened Canaries - stuffed 7-0 at the Etihad Stadium in November - who raised their game and soaked up plenty of pressure to earn what for them could be a crucial point in their fight to stay up.
Despite dominating for large spells, City failed to create many clear openings after hitting the crossbar in the first half through a header from Alvaro Negredo.
Norwich - who had seen a first-half effort from Gary Hooper ruled out for offside - almost snatched victory in stoppage time when Nathan Redmond's cross flew through the six-yard box just ahead of Ricky van Wolfswinkel.
City are now in third place, two points behind new leaders Chelsea.
Manuel Pellegrini: "I don't know if it's a missed opportunity because today Norwich played a very good game. They defended very well and we couldn't score.
"I was concerned about this match and it was exactly the same when we played Chelsea because we have a lot of players who are not 100% fit.
"Maybe it was a good opportunity, but we are still two points behind the leaders.
"Toure played today in a defensive role and that's why we lost a little bit in attack, but at the moment Fernandinho and Garcia are not fit.
"It's exactly the same with our strikers, with Negredo and Dzeko, but I don't think that's the reason why we didn't score in the last two games.
"They are not 100%. Dzeko has an ankle in a very bad condition which is why he played just 30 minutes and Negredo has a problem with a shoulder but they had to play in that condition.
"Yaya had to play today a little bit back because we did not have another defender who could play in that position.
"Everybody has been talking about how many goals we score and how we concede them when we defend, but the most difficult thing is scoring goals.
"In the last two games, with our strikers not being fit, we couldn't do it and without a goal you can't win a game."