The Paraguay international, who played under Pellegrini at Malaga last season, is convinced the Chilean has all the credentials City were looking for in a new boss.
Pellegrini replaced the sacked Roberto Mancini in June with City hoping he can build on the 2012 Barclays Premier League title win by claiming more trophies, playing better football and improving dressing-room morale.
Santa Cruz, who has now joined Malaga permanently after being released by City, told Fox Sports Asia: "It is a tough call because I think Mancini was successful and brought the club forward two steps, in terms of winning trophies.
"It is tough to sack him after his success and I think the fans realise that he deserved to continue.
"But the club keeps moving forward and has high expectations.
"They are obviously chasing the Champions League next and there are few managers in the market that can deliver that.
"Pellegrini deserves the chance to win titles and be successful.
"He has great qualities when it comes to managing so many stars, a high-profile dressing room.
"The way that he is as a person - relaxed and calm - will make players feel important and part of the City project.
"He is good with squad rotation and a guy who can put everyone on the same ship."
Santa Cruz, 31, scored eight goals for a Malaga side that reached the quarter-finals of the Champions League last season.
That success in Europe was one of the factors that attracted City to Pellegrini and Santa Cruz was ideally placed to pass on his knowledge of the English club.
Santa Cruz said: "He did not ask for advice as such but we did speak about the dressing room.
"He is one of those guys who really takes a lot of care when it comes to how healthy the dressing room is in terms of friendship and good guys.
"He was very interested in knowing how the guys are.
"He also had his fears - going into a league he did not know too well - but it won't be hard one bit for him because of the type of person he is.
"Also the guys in the dressing room are nice and friendly and will welcome him."
Santa Cruz joined City from Blackburn in a £17.5million deal in 2009 but, hampered by injury, scored just three goals in 20 games for the club.
He had loan spells back at Blackburn, Real Betis and Malaga before his City contract expired at the end of last season.
Although his City career did not work out, he insists there are no hard feelings.
He said: "I have no regrets but it was tough with my knee - just bad timing at City.
"I wish I did not have it or I could have recovered quicker but no regrets because I worked hard to get fit and be successful with the team.
"They were successful without me which I am very happy about - for Mancini and his people and the players."