Goals from City old-boys Jack Rodwell and Adam Johnson cancelled out efforts from Yaya Toure and Stevan Jovetic at the Etihad Stadium, as the champions threw away a two-goal lead for the second time in as many Premier League outings.
However, unlike in their draw with Burnley on Sunday, City had the final say as Frank Lampard's late header helped his side to maximum points.
Pellegrini was frustrated by City's second-half stumble but praised his side's character for finding the winner.
"We played a very good game over 90 minutes," said the Chilean.
"Maybe in the first half we were very patient, we pressed very well and didn't give any chances to Sunderland to score.
"The only thing we talked about with the players at half-time was that we didn't make the correct movements in the final third to score when they have 10 players behind the ball.
"We scored two beautiful goals with great movement but after that it is difficult to understand.
"Maybe the corner I can understand because they have very tall players and are very dangerous from set-pieces.
"The penalty was too easy for them, but once again this team had the personality and character to go for the third goal.
"We had three or four clear chances to score more goals and in that sense [goalkeeper Costel] Pantilimon was their best player."
Pellegrini also played down the importance of matching fellow title-chasers Chelsea, adding: "We are not trying to win to keep the pressure on Chelsea, we try to win to keep playing the way we are doing so far.
"At the end of the season we'll see who has more points but it is not to make pressure for Chelsea it is just to win our games."
