Carrick, who has been hired to the end of the season, has overseen victories over Manchester City and Arsenal in his first two games in charge.
But Scholes said on The Good, The Bad & The Football podcast: "He’s come into the job now and it’s been that bad for a year that it couldn’t really get any worse so the pressure isn’t really on you while you’re interim manager.
"Once you take that job full-time, at the start of the season next year, let’s say, all of a sudden you’ve got to be winning games straightaway.
"They will be scarred a little bit from the Ole (Gunnar Solskjaer) thing. If the Ole thing hadn’t have happened then it would probably be more likely.
"But if Michael has got to go up against, say, Thomas Tuchel in the summer then there’s only one winner if you’re looking at coaching big clubs and winning big prizes so you can’t really compete with that."