Mancini led his side to a 6-1 humiliation of defending champions United at Old Trafford on Sunday and in the process cemented their place as favourites for the Barclays Premier League trophy.
Wright believes the win will only spur on the most experienced manager in the league and Mancini must be prepared for it.
Wright wrote in his column for the Sun: "Roberto Mancini is about to face his toughest ever test as a manager - dealing with Alex Ferguson's mind games.
"Kevin Keegan cracked under the pressure when taking on Fergie while even Arsene Wenger has struggled at times over the years.
"But after Sunday's unbelievable win at Old Trafford, Mancini will find himself in a position he has never experienced as the old master uses every tactic in the book.
"On a weekly basis, Ferguson will now look to pile the pressure on City and increase the expectation of the club's supporters."
Wright concluded that while Mancini has managed big sides like Fiorentina, Lazio and Inter Milan in the past, he has never had experience handling the wrath of the fiery Scot.
He wrote: "I'm a massive fan of the United manager and his team. They will definitely recover from this hammering.
"You can be guaranteed that Fergie will keep stressing that the title is City's to lose. They are the favourites. That United have a long way to go to catch City.
"City, and I don't like this term noisy neighbours by the way, are in a terrific place right now.
"But they know that if they make any slips, then United will be right there breathing down their necks.
"Mancini's men still have to go to Liverpool, Chelsea and Arsenal and win.
"And Mancini faces a battle to deal with the fact that many City fans now expect to win the title even though there is a long way to go."
However, Wright stressed that he does not believe the rival managers will engage in any verbal sparring over the campaign because there's too much respect between the pair.
Wright wrote: "A bit like Jose Mourinho, I think Mancini has a lot of respect for Fergie so I'm not sure whether they'll have any verbal spats over the season.
"But you can be sure, when the time is right, Fergie will lob the odd grenade towards City's training ground.
"I didn't think United played to their normal levels but you cannot take anything away from City. They were absolutely brilliant.
"City didn't fear United, which I loved, and this result will never, ever be forgotten by both sets of fans.
"But Mancini's players now face this major test over whether they can maintain the consistency you need to win the title.
"United's training ground will be an interesting place over these coming days, weeks and months.
"They will put everything into getting things right and you can be sure they'll be prepared when they make the short trip to play the return at the Etihad Stadium on April 28. That will be a fantastic match.
"For City, the war has only just started. And for Mancini, the mind games are just around the corner."
United are currently five points behind leaders City in the Barclays Premier League and will travel to Aldershot Town on Tuesday in the fourth-round of the Carling Cup.
City are away to Wolves in the same competition on Wednesday.