The Scot has endured a frustrating start to his tenure as United boss since replacing Alex Ferguson at Old Trafford in July.
Back-to-back 1-0 defeats at home to Everton and Newcastle United followed consecutive 2-2 draws with Cardiff City and Tottenham, a run that has left United in ninth position in the Premier League, some 13 points adrift of leaders Arsenal.
With champions United struggling to maintain pace in the race for the title, Moyes has been advised to enter the transfer market when the window re-opens in January.
But Schmeichel - who won the Premier League five times in an eight-year stint at Old Trafford - believes that is not necessarily the best way to proceed, urging Moyes to lay down the law by removing players who are not performing to their full potential.
Speaking to talkSPORT, he said: "What I think is really important to David Moyes is maybe not bringing players in, but letting players go.
"It is very important he stamps his authority on the squad and some of the players that are there are not performing well enough, and it has been going on for a while.
"It would be much better for the club if he brings one or two of the younger players through and lets one or two go."
United have the opportunity to get their season back on track in Sunday's visit to Aston Villa.
