The Chilean believes that Everton are among the contenders for the title this season.
Everton were one of the Premier League's surprise packages last season, shaking of the losses of manager David Moyes and prized midfielder Marouane Fellaini to secure an impressive fifth-placed finish.
With the resurgence of Liverpool, the steady improvement of Arsenal and the resurrection of Manchester United under Louis van Gaal, most would expect Everton to hover around the Europa League places in 2014-15.
"Chelsea, Liverpool, Arsenal, Tottenham and also Everton, they can all challenge," the Chilean said in an interview with Sky Sports News.
"Everton had a very good season last season and they will continue to play that way with Roberto Martinez who has a strong squad."
Pellegrini could simply be taking the pressure off his side as they look to defend the title next season by talking up the opposition, but it is a testament to Everton's performance last season that they are in the conversation.
Much of last season's success can be attributed to Roberto Martinez's arrival. The Spaniard brought his own brand of patient, possession-based football to Merseyside and saw immediate results.
The Toffees were one of the least direct teams in the Premier League last season, a complete departure from the David Moyes years, and they scored far more goals as a result. Everton ranked sixth in the Premier League with 61 goals, behind the top four and Manchester United.
Martinez's side were also excellent defensively - only Manchester City and Chelsea conceded less goals in the Premier League last season.
Everton could certainly carry that level through to next season. They have held on to their best players in this transfer window, and managed to secure the signing of Romelu Lukaku on a permanent deal from Chelsea.
Lukaku is one of the true top-class talents in the Everton squad, the type of player any team in the league would want. He netted 15 times last season and recorded six assists, and at the age of 21 he will only get better over the next few years.
Another player who could make a huge difference next season is Ross Barkley. The England international showed flashes of brilliance last season, and another year of top flight football could see him blossom into one of the division's top playmakers.
What will hold Everton back, however, is their lack of depth in key positions. Behind Lukaku they lack a quality striker to carry the load - Kevin Mirallas is more suited to play on the wing and Lacina Traore is a work-in-progress.
In the middle of the park it is hard to imagine Gareth Barry replicating his form from last season. He remains a solid holding midfielder but at 33 years of age he cannot be relied upon for an entire season. The Toffees also lack another creative midfielder to support Barkley, who is bound to have off days at his young age.
The title often comes down to two key factors - strength in depth and championship-winning experience. Those qualities separated Manchester City from the pack last season, and were the driving forces behind the title-winning Manchester United sides under Sir Alex Ferguson.
Everton will almost certainly be as good or better than they were last year, but the strength of their rivals and their lack of world-class players will see them fall short at the business end of the season.
Do Everton have the squad to mount a Premier League title challenge?