Carrick was in the United team when Sanchez scored twice in a 3-0 Arsenal win at the Emirates in October 2015 and the 36-year-old believes the former Barcelona man will come good at his new club.
Raphael Honigstein has revealed the real reason why the Arsenal dressing room hated Alexis Sanchez so much.
"I said when he first signed, he is a Man United player, he suits the way we play, he has got that excitement, he always looks forward, he is dynamic and in the end you can judge him in the first few games or whatever but I think over time he will be terrific and I have no doubts about it".
"They really felt that he was just playing up to the camera, doing all these things like, 'oh, I'm trying, but no-one else is, what am I doing here?' And then, quite tellingly, Wenger, he talked about this a year ago, at Arsenal, they put up stats inside the dressing room after every game, showing the amount of kilometres run, and Sanchez would regularly come out with the lowest by a big distance". In these games, you've got to go and take the game by the scruff of the neck.
"If Pogba's going forward and Sanchez is dropping, you can nearly throw a blanket over them - and that will be music to the ears of opponents".
"It's going to take a little bit of time for Sanchez to adjust".
"You have to give the fans something to shout about".
Sanchez's form towards the end of his Arsenal career was not great.
"They looked like a team thrown together, full of strangers". However, Sanchez has endured a hard first few months at Old Trafford. When you go to a [new] team you don't lose all of your talent, it's still there. Sanchez has not fitted into the Red Devils team and he must start having an impact.