City remain five points behind Mourinho's Premier League leaders despite placing Chelsea under siege for much of the contest.
Thibaut Courtois' uncharacteristic error led to David Silva's equaliser before half-time.
Just a few moments earlier Loic Remy, deputising for the suspended Diego Costa, had given the hosts the lead.
Chelsea were encamped in their own half for much of the match and will be more satisfied with a point which leaves them in pole position for a first title in five years with 15 games to go.
Pellegrini, who called Chelsea a "small team" after September's 1-1 draw in the reverse fixture, questioned Mourinho's approach afterwards.
The City boss, the only manager to speak post-match as Mourinho continued his blank of the media, said: "Both teams have a clear style of play
Everyone wants to play in the way they think is better.
"He has a style
You analyse the style of Chelsea
I analyse just the style of my team.
"Our team tried to win the game from the first minute till the end
I'm very proud about that.
"It's not easy to come here, to Stamford Bridge, against the leaders of the Premier League, with very good players.
"We create, especially in the first half, clear chances to deserve more than the point.
"That's why I'm not happy about the point but I'm happy about the performance of the team."
Pellegrini praised Chelsea's defensive efforts, too.
"From the first minute we came for the three points," he added.
"We made some changes to continue trying to create space against a team that defended very well, very near their box and is very dangerous on counter-attack.
"We couldn't just think about attacking
That was the most important thing of the game, that they didn't have any chances to have those fast counter attacks that they always do.
"I don't think Chelsea played for a draw
I just said our team played to win."
City were the first team to emerge undefeated from Stamford Bridge in the Premier League this season, ending the Blues' 10-match winning run.
And Pellegrini maintains his side are capable of overcoming the deficit in the remaining months of the season.
"Of course it was important to try to close the gap," he said.
"We tried, but we couldn't
We still have 45 points more to play (for).
"This was a very important game, it was not a final
We have time to try to recover those five points.
"If we continue playing in the way we did today, I think will be more easy."
Mourinho, who cancelled his usual Friday pre-match media conference in apparent protest at Costa's three-match suspension for stamping on Liverpool's Emre Can, again declined to speak publicly.
Midfielder Nemanja Matic told Sky Sports 1: "To be honest we expected three points, but I think the draw is a good result for both teams.
"It's the same (gap), five points, and we are happy because of that.
"City showed they are very strong, they never give up and scored in the last minute of the first half."
Matic added that his side's extra-time clash with Liverpool in midweek, when Chelsea advanced to the Capital One Cup final, had taken its toll.
"I am happy with how we played but we did our best after a hard game of 120 minutes," he added.
"We felt it especially in the last 20 minutes, a little bit tired, but I am happy because everyone gave 100 per cent."
Frank Lampard, Chelsea's record goalscorer after 13 years at the club, scored the equaliser in September's contest, but was unable to make a similar impact on his Stamford Bridge return.
Bar a few dissenting voices, Lampard was given a fine ovation and embarked on a lap of honour at the end - something he was denied when he left the club for New York City FC last May.
"There were more chances for City in the game, Chelsea had a big old game in midweek and the draw probably suits them in the long run," Lampard said.
"It was a solid game and Chelsea probably accepted a point in the end.
"This doesn't change anything
Chelsea will be happy to be five points clear, we're not stupid, we know what that lead is
But there are lots of points to play for."
On his own reception, he added: "The Chelsea fans showed complete class at the end
I enjoyed this."
Source : PA