Speaking on Sky Sports, Carragher said: "I feel like I've been talking about Marcus Rashford for the last week, and I've said before, he's not that good of a player for the amount of time that we talk about him. Wayne Rooney was, David Beckham was, Cristiano Ronaldo was.
"I'm not for any player coming out and being critical of the club, but for Rashford to do that, to come out without the club having any knowledge of it and just announce he's basically put in a transfer request or he wants to leave the club, that leaves the club in a really poor position in terms of negotiating his exit at some stage.
"If he really believes he wants to still be a Manchester United player and he still wants to have a great career, you don't come out with a statement like that. You keep your mouth shut, you battle and you hope that you get a little chance."