United ended a four-game losing streak against their city rivals in emphatic style on Sunday as they came from behind to secure a sixth straight Premier League win.
The defeat is City’s sixth in their last eight matches but Pellegrini would not be drawn on his future and instead decided to focus on his side’s failings at Old Trafford.
“My future is not the most important thing about what happened today,” he told Sky Sports.
“I’ll continue working. We have to play six more games to try to finish as high as we can and, for me, that’s the only thing that’s important.
“United played very well after the first 20 minutes in which we played very well. We scored a goal and had two or three more clear chances to score but we didn’t and they started growing.
“We didn’t continue playing the way we started the first 20 minutes and we lost the marks, we couldn’t continue playing against a very tough Manchester United.
“Their equaliser was special play because it was a clearance from their goalkeeper, Pablo (Zabaleta) slipped and they scored. From that moment, they grew and started playing better.”
United led 2-1 at the break and extended their advantage with a third after 67 minutes, although scorer Juan Mata appeared to be offside in the build-up.
But Pellegrini was more critical of his own side than the decision to award the goal, saying: “I do not want to analyse the referee’s decisions. They have to do their work, maybe the third goal was offside but it was one thing that happened during the game.
“That happened in the other game where we lost by an offside goal, but I’m not talking about the referee.
“I don’t think the analysis will be about the refereeing decision. Our mistakes for at least two of their goals and the fact we didn’t take our chances to score another goal at the beginning of the game will.”
The Chilean did admit, though, that the third goal was crucial as City slipped four points behind their rivals in the table.
“The third goal was the decisive moment,” he said. “Once they scored their third, we had to take more risks and they had space and they won the game.
“United’s pace wasn???t the problem for us. It’s easier for a team to play with pace when they have two goals in front and possession of the ball.”