The Red Devils put in another below par performance as they were beaten by Newcastle 1-0 on Saturday night.
It leaves United seventh in the Premier League table and they are also in huge danger of crashing out the Champions League in the group stages.
Rashford scored 30 goals in all competitions last season but has struggled this term, finding the back of the net just twice in 18 matches.
Carragher slammed the England star's lack of leadership qualities when discussing United's loss to Newcastle.
The Sky Sports pundit brutally compared him to team-mate Anthony Martial, who "doesn't care" about the club.
Carragher said as cited by Sports Central: "It looks like there are big problems. "Watching Rashford, that was an unacceptable performance for a few reasons. "That lad didn't play midweek in the Champions League [versus Galatasaray], but I have been a local player and it's not easy especially when the team is not doing well. "For Rashford and myself and Steven Gerrard at Liverpool, it's your job to fix it and drag others up with you.
He added: "Watching Rashford he reminds me of Martial and that is the worst possible thing you can say about him. "Foreign player comes in and doesn't really care. Rashford is now looking like Martial. "As a local player you do not stop running for that badge and your supporters as you are supposedly one of them."
Rashford played just 61 minutes before he was subbed off against the Toon.
He has since been slammed by Paul Scholes and Alan Shearer.
The Newcastle legend and pundit claimed he "didn't look interested" on the pitch.
And manager Erik ten Hag is preparing crunch talks with Rashford to fix his dismal form.
Meanwhile, Gary Neville fumed at the entire club, ranting: "I don't want to do their games anymore, I don't want to watch their games anymore and that is the saddest indictment that you can have of your football club."
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