Carragher believes United are getting even worse under manager Louis van Gaal as they look set to miss out on Champions League football for a second time in three years.
Van Gaal has spent plenty of money as his second season at the club draws to a close and, despite the outlay on new players, he looks set to lead them to a worse finish than the fourth place he achieved in his first season.
"It looks like they're going backwards," Carragher told Sky Sports.
"In terms of Louis van Gaal, I don't see him at the club next year if he doesn't get top four."
Carragher took particular issue with the way Van Gaal praised his side after the game.
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"Manchester United are a much bigger team than Tottenham, although Tottenham have a better side at the moment, and [Van Gaal] is talking about how well they played," he said.
"The fact we're saying United played well, we even mentioned it at half-time. That's United playing well now, without ever looking like scoring in that first half.
"[Tottenham] could have scored five or six today. [Anthony] Martial had the one chance at 0-0, but that's what it's come to now, where Van Gaal is actually pleased that they just gave Tottenham a game.
"That's what he said: 'Before the first goal we've given them a good game', but this is Manchester United and they're talking about Tottenham as if they're Real Madrid!
"I'd be worried listening to my manager speaking like that after a game."