Eden Hazard's first-half penalty was the difference as the 'Blues' secured the FA Cup crown over their Premier League rivals at Wembley on Saturday.
Analysing the game for 'BT Sport', Scholes was very critical of Sanchez's dismal display for the 'Red Devils' and overall since he made the switch in January.
He said: "His performances, well they have to improve. They can't get any worse to be honest with you.
"I think the next few games of next season are vital for him, he needs to get fans believing again and believing they are going to get close to City. They need a big player".
Scholes continued: "Do they [have big players]? Paul Pogba doesn't win you games on his own. Hazard does. Sanchez doesn't, he's shown since January, they thought he could, but not from what we've seen.
"They need two magical players. I think they've got really good players, they haven't got Hazard, Cristiano Ronaldo or Lionel Messi, and I know many teams haven't, but the difference between the two was Hazard's quality".