Pellegrini said that the win over United was huge for the club, but that his side would need to play as well if not better to beat Arsenal in the next game.
"It was very important for the fans, club and players to win the derby," BBC Sport quotes Pellegrini as saying.
"Now we must continue and look to win the next match. Arsenal have very good players and we will need to play a very good game if we are to win."
City are currently third in the Premier League, but would go three points clear if they win both their games in hand.