England winger Grealish completed his transfer from boyhood club Aston Villa to City this week and could make his debut from the bench in Saturday's Community Shield.
Villa confirmed they had received £100m from City for their captain, triggering a release clause and making Grealish the Premier League's first nine-figure signing.
That is a select group across Europe, including the world's most expensive player Neymar and Paris Saint-Germain team-mate Mbappe.
"Jack Grealish has become part of the Neymar 100 million, Mbappe 100 million, [Philippe] Coutinho [group]," ex-Villa captain Petrov, one of the founders of Player 4 Player, told Stats Perform.
"So now he is not just a UK star and brand, now he's become global. Now he's become even bigger because now he is compared with one of the best.
"All the eyes will be on Jack now. Jack has to understand that the hard work starts now.
"In a team like Manchester City, every single player there is a top player. So, you have to go there, you have to adjust your game, you have to be at the top of your game every single time.
"If you don't play well every single week, the next [player] is waiting for your spot. When [they take] over, sometimes it takes months before he comes out again because the team is so well drilled and they just win games.
"So, Jack has a huge challenge. But when you are a top player, when you are a player with his abilities, you are always willing to challenge yourself.
"That is probably one of the reasons that he moved on, because with everything we will be reading in the press about Villa looking after him, Villa offering him a new contract, I think that Villa have done everything in their power to keep Jack Grealish.
"Unfortunately, that offer came at the time he has to make a decision to develop in a different way or stay at the club that he loves."
Petrov added: "He's got the platform now. He just needs to go and take it. Because the platform is there. He is at Manchester City. Manchester City will be fighting, will be challenging for every single trophy, at every single season.
"It is down to him how he is going to look after himself, how he is going to prepare for different dynamic of the season.
"Because at the moment, Jack will have another challenge as well; he only played in the Premier League and in some club games, but now he has to adjust to more travelling, with the European games, more games, more intensity, more demand.
"So, this is something that he has to adjust. But now he has the platform. If he can manage to use it, anything is reachable for this boy."
Forging a role in the team is another challenge, with Kevin De Bruyne and Phil Foden last season often taking up the left-sided positions Grealish likes to occupy.
But Petrov said: "He has got the ability to fit in any position.
"Pep Guardiola is a completely different manager from anybody else; he gets the quality of the player and he uses it in a completely different way.
"I could give you a premier example with Foden. Everybody says that the Foden position is in the middle and he plays on the left, the wide left, and the wide right.
"So, Jack Grealish will be the same. [Guardiola] will just develop and teach Jack Grealish to play in a number of positions.
"Can Jack Grealish adjust to that? He can. Certainly. Because he has got the ability, he has got the knowledge and the awareness to do those positions.
"I believe when Pep Guardiola spoke to Jack Grealish, he would have told him how to play number of positions, how to develop his skills, his ability, but also how to fight to be one of the best players in the world.
"And I believe that was what Jack was wanting: somebody to tell him that he is going to be in the spotlight, people will be talking about him.
"He needed more persuasion. That was what he needed. Just to show him that he can fight to be one of the best."