Jose Mourinho's men were on the back foot for much of Sunday's clash with their Premier League title rivals, but went 1-0 up through Andre Schurrle thanks to a lightning counterattack in the second half.
However, the 10-man hosts claimed a point when Frank Lampard popped up with a goal in the 85th minute, denying his former club their fifth victory of the new season.
Pellegrini expressed dismay at the visitors' defensive tactics after the game, comparing their efforts to Stoke City, who earned a shock 1-0 win at the Etihad Stadium last month.
"I'm not satisfied with the result today," the Chilean said.
"I think we played 90 minutes against a small team just trying to defend, trying to just to keep 10 players in front of their goal.
"[We were] the team that wanted to win from the beginning, we had two or three clear chances especially in the second and after we went down to 10 players we continued trying to win.
"That is why I'm satisfied with the performance of the team but not so satisfied with the score.
"I don't want to analyse Chelsea. I think we played against the same team as we played against Stoke here.
"It was very difficult for us to score but what the other teams do - it's not my duty to analyse."
Pellegrini went on to praise the efforts of midfielder Lampard, who refused to celebrate his goal against the club where he spent 13 years of his career, becoming their record goalscorer in the process.
"When I sent Lampard on I told him to go and score," he added.
"I was so sure he'd play well against Chelsea because he's a very good professional and he always wanted to be involved in this game from the beginning.
"I spoke with him at the beginning of the week and he wanted to be involved, he's a very good player and a great professional so I am very happy for him."
