The Red Devils have endured an unspectacular start to life under David Moyes and have lost their last three matches, while neighbours City are just a point behind leaders Arsenal and top the goalscoring charts.
And Pellegrini says he is only focussed on his own side and has little interest in United's current problems under Moyes, though admits they pose far less of a threat than Arsenal or Chelsea in the title race.
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“Maybe it's a strange season for them but we are not thinking about that. I don't think we are living better because they have troubles or problems.
“We try to do our best and we are not worried about our neighbours.
“Of course the major rivals in this moment are the teams that are very near. Arsenal that is top are one point above us and Chelsea are one point behind.”
City have not lost in their last 14 games – a run which includes victories over Bayern Munich and Liverpool – and Pellegrini believes defeats against Cardiff and Aston Villa earlier in the season helped shape the side's style and mentality.
“A lot of managers can manage the way they want,” continued the former Malaga boss. “There's not just one way to do it.
“Maybe other managers would see their team score one goal and then prefer to go back and counter attack, than try to score the second goal.
“But for me it’s very important to continue the way I play. I’ve been the same my whole career.
“You have clear ideas about what you want. I remember when we lost at Cardiff and Aston Villa, I wanted them to continue in the same style.
“The only way is to have a style of football. We could have had a better chance if we’d played against Cardiff and Aston Villa with 10 players behind the ball.
“But I was sure in that moment it was impossible to improve in that way. We lost, but for the players it was important to understand we were not going to change our style.”