Pellegrini issues City ultimatum over style
City trail Premier League leaders Liverpool by six points – albeit with a game in hand – and only have the League Cup trophy to their names this season.
If they fail to win the league, the Chilean could come under pressure to keep his job from the club's rich owners.
Pellegrini said he wanted to see his team play attractively to win the title, and was willing to accept his sacking if the owners wanted otherwise.
"The way I want to win the title would be to be the best team of the year, to play attractive football for the fans, to be a team with character and personality," he told the Sunday People.
"If that is not what is wanted then maybe another manager comes here who wants to play kicking the ball high, trying to score just one goal and the game is over, and every week complaining about the referee.
"You can have a little advantage with some unfair play but I don't think it's the way to do it.
"After the game at Liverpool (which City lost 3-2) it would have been very easy for me to talk about the referee. It was the most important game of the year but I didn't say anything about the referee."
Pellegrini, whose side face Crystal Palace on Sunday, was appointed by City on a three-year deal in June last year.