The 43-year-old Red Devils legend made his debut for the club in 1992, going on to win eight Premier League titles, three FA Cups and two Champions League.
“Gary Neville once told in me he felt he only ever played with two genuinely world class players in his Manchester United career,” Carragher wrote in his Telegraph column.
“One was Cristiano Ronaldo. The other was Peter Schmeichel. That is how fundamental he was to United’s success.”
Schmeichel is often widely regarded as United’s greatest-ever goalkeeper, while Ronaldo is arguably the club’s best-ever winger.
The duo stood out from others during their respective reigns at Old Trafford, and they helped define Sir Alex Ferguson’s trophy-laden time in the dugout.
There has been a dearth of world-class players at Manchester United since the Scottish legend left, and Spanish goalkeeper David DeGea is seen as the only true star in the side due to his consistency over the years.
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