Manchester United collapsed in the second half at White Hart Lane.
Manchester United collapsed midway through the second half against Tottenham, potentially killing off their hopes of finishing in the top four.
This means another campaign without Champions League football, for the second time in the last three seasons.
He criticised the Argentine international defender for his poor marking at the set piece from which Toby Alderweireld headed home Tottenham's second goal, minutes after Dele Alli's opener.
Carragher told SkySports 1's post-game broadcast: "The defending from Rojo is embarrassing. He doesn't even jump or make a challenge."
The ex-Liverpool defender went on to pick out teenager Timothy Fosu-Mensah as 'United's best player,' during the game.
Fosu-Mensah certainly played well, but the problem was that as soon as he was substituted with a slight injury, United looked a poorer side.
The Red Devils conceded two minutes after the young Dutchman was taken off, with Tottenham concentrating their attacks down the side of his replacement, Matteo Darmian, who struggled to get up to speed.