In recent times, it hasn't worked out too well for the team trying to defend their title, with Manchester United finishing 7th in the table last term.
Pellegrini says City didn't do so well when it was their turn.
Meanwhile, Liverpool boss Brendan Rodgers says he's searching for another new striker, despite a 2-1 win over Southampton in their opener.
Rickie Lambert joined in pre-season, but Rodgers wants more firepower to replace the departed Luis Suarez.
He says Daniel Sturridge, who scored at Anfield, is hardly a bad existing option in attack.
Tonight Chelsea open their campaign away to Burnley at 8.