Victory at Everton on Monday night leaves United in fourth place, three points behind third place Aston Villa and three ahead of Chelsea and Liverpool in fifth and sixth place respectively.
Carragher said at the final whistle: "I think Manchester United are a virtual guarantee now because Aston Villa look like they are dropping points at the moment. They have still got European football on Thursday nights, so there's a lot of Thursday-Sunday football.
"Liverpool and Chelsea still have Champions League football and the FA Cup, and they will want to do well in at least one of those competitions, semi-final or final stage.
"So I can't see Manchester United not making it."
On United matchwinner Benjamin Sesko, Carragher added: "Sesko has gone over 80 yards and then finishes, you expect him to be breathing heavily ad panting after it, but no, he still has the energy to really celebrate.
"He's had maybe a slower start than he would have like initially, but he has been on fire of late.
"We were wondering whether he would start tonight, it almost feels inevitable now. He has put himself into the team."