New manager Erik ten Hag has changed the mood around United
Ten Hag’s strict fitness regime and new approach has served up good performances that included a 4-0 win against a second-string Liverpool side on Thailand earlier this month.
Yet Carragher has told Sky Sports that Ten Hag faces a huge job to get United back into the title race after a disastrous campaign saw them finish more than 30 points behind Manchester City and Liverpool last season.
“I think there's a long road for United that they're on at the moment in terms of challenging for the title,” said Carragher.
"I think the first thing when it comes to Ten Hag and the players they're bringing in will be, 'we need to get this club back in the Champions League where it belongs'. That's where Manchester United should be.
"They're one of the biggest clubs in the world, never mind this country, so to not be in the Champions League just doesn't feel right, not when United are in the Europa League.
"So I think that's the first thing and I think once United do that, then it'll be looking at the title in the next couple of years.
"But it won't be easy to get back in the top four this season - not just for United but for any team who are normally in the top four.
"You'd expect [Manchester] City and Liverpool to do it because they're always going for the title, but you look at how strong Chelsea will be and the signings they're bringing in, Tottenham's work as well, Arsenal also.
"So I think competitively now in terms of getting in the top four, it's really tough, and it's proven that way for a lot of Manchester United managers with great CVs in the past.
"But there's no doubt this manager has a really good CV and they made a really good start in pre-season."