The North-West outfit earned their second league title in three years last season, finishing two points ahead of Liverpool.
However, with Chelsea, Manchester United, Arsenal and Liverpool strengthening their squads this summer, the new campaign is expected to be tight at the top.
"It's a big challenge because in the Premier League you have five or six teams with very strong squads," Pellegrini told Sky Sports News.
"All of them want to win the title so that's why it's very important for us not to live with what we did this year. If we want to win the title we have to fight from the start until the end."
City will open their campaign with a clash against Newcastle United on Sunday.