The Premier League champions initially found themselves trailing at home as Wilfried Bony gave Swansea an early lead, but they eventually fought back and claimed all three points, with Toure grabbing the winner.
Stevan Jovetic brought City level in the 19th minute, before Toure scored the decisive goal with just over an hour played.
Swansea almost snatched a late equaliser through Bafetimbi Gomis, but the hosts held on and Pellegrini was particularly happy with Toure, who endured a busy international break for Ivory Coast with games against Sierra Leone and Cameroon.
He said: "I think it's important for Yaya [to have played well] - he played for his national team on Wednesday and he played two games in a week but he had the personality and character to continue playing until the end.
"I think he played very well but we can't analyse Yaya on how many goals he scores. It's impossible for him to score the amount of goals he scored last season. Yaya's a midfielder, not a striker.
"It's important for him to play well and I think he's improving every game."
Up next for City is the visit of Bayern Munich in the UEFA Champions League and, although Pellegrini was content with Saturday's performance, he acknowledged that his men cannot afford to make the same mistakes against the Bundesliga champions.
He added: "It's important for the Premier League as we had to add more points. We have seven games in December which means there are 21 points to play for and we have to win as many as we can.
"After that, it's always better to arrive into the Champions League against a great team like Bayern, winning rather than losing.
"Maybe if we scored before our second goal, we wouldn't have had a nervy last few minutes. But for different reasons, we struggled to make the last pass and their goalkeeper made important saves.
"We're working every day to improve defending, so I hope on Tuesday we won't make the mistakes we made today."
