Jose Mourinho's Premier League leaders went ahead when Loic Remy broke the deadlock in the 41st minute but David Silva responded for the champions in the final minute of the first half, ultimately ensuring that the gap at the summit remains at five points.
City created the clearer openings in a game of few chances before Remy's opener - Chelsea's second and final shot on target as the visitors dominated play after the interval but were met with stubborn and disciplined resistance.
Pellegrini, who has a frosty relationship with Mourinho dating back to their time in La Liga, criticised Chelsea for playing like a "small team" when the two sides drew 1-1 at the Etihad Stadium in September.
He refused to directly comment on Chelsea's tactics on this occasion but pointedly mentioned his team's attempts to force victory throughout a 90 minutes when the hosts faded as an attacking force.
"I think that our team tried to win the game from the first minute until the end," he said.
"I am very proud about that because it is not easy to come here to Stamford Bridge against the leaders of the Premier League with very good players.
"We created, especially in the first half, clear chances to deserve more than the point.
"That's why I am not happy about the point but I am happy with the performance."
Asked whether Chelsea needing extra time to secure a League Cup semi-final victory over Liverpool in midweek caused them to tire, Pellegrini said: "I don't know what happened with Chelsea. From the first minute we came for the three points.
"We made some changes to continue trying to create space against a team that defend very well, very near their box, who are also very dangerous on counter attacks - we could not think just attacking.
"That was the most important part of the game - that they didn't have any chances to have those fast counter attacks that they always do.
The Chilean added: "I think that both teams have a clear style of play. Everybody wants to play in the way they think is better.
"You [journalists] analyse the style of Chelsea; I analyse just the style of my team. I repeat I am very proud of the way we played away against the leaders of the Premier League. It is a difficult stadium where Chelsea normally wins.
"I'm not saying we are more attacking, I'm saying that both teams have a clear style in the way they play. You must analyse the style."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.