Rafa Benitez was unable to lead Chelsea to victory in his first fixture in charge, which saw Sergio Aguero go closest in a game of few chances.
"I think we play very well but are missing a goal," Mancini said. "We had a lot of chances but were missing the last pass or shot.
"When you are near the box you should be very strong, if you are soft you cannot score.
"We dominated the first half, second half Chelsea did better, but we need to be strong, we were too soft.
"Games here are always hard but today we played well while missing the last pass.
"Last year we lost a good game, this year we took one point. I am not happy but I prefer this."
Asked if it was a point gained or two dropped, Mancini replied: "Two dropped."
His counterpart Rafa Benitez was roundly booed in his first game as interim Chelsea boss.
Mancini admitted he had never heard such booing for a new manager from his own supporters.
He said: "I work with another team. But I can say it's very difficult for him and for his team to play well.
"I don't think that Rafa is a magician. I don't think he can change everything in a few days.
"Weeks ago, Chelsea were on top and playing well. They have good players. Every manager needs time."