He said: "It's hard to win the Premier League as our top four sides, plus Barcelona, probably make up the best five sides in Europe.
"But that's the challenge we face as United face their own challenge in carrying on without Ronaldo. He's a great player and I think he will be a big miss for the Premier League.
"He made a big difference to Manchester United, even though they have a lot of other great players. And I think he was one of them. We all know it will be difficult for them to replace Ronaldo, no doubt.
"But maybe they will do it a different way and get two or three players. But, as I've said, it will be so difficult to replace someone like him.
"Hopefully they won't bring in someone as good as Ronaldo."
And in a playful dig at Sir Alex Ferguson for agreeing to let his prize possession flee to Spain, Carragher added: "I'm sure Sir Alex knows what he is doing "