The Red Devils were in impressive form at the King Power Stadium as goals from Henrikh Mkhitaryan, Juan Mata and Zlatan Ibrahimovic handed them their first win in three Premier League outings.
The result left Manchester United in sixth place in the Premier League table but just a point behind fifth-placed Liverpool as the race for Champions League qualification hots up.
Speaking to Sky Sports after the game, Carragher said: “They’re on a great run. I think they’ve been in great form. They are where they are because of the start to the season they had but they’ve got great momentum now.
“This will give them a massive lift especially on the back of the Liverpool and Arsenal results.”
He continued: “Despite the run Man United have been on, you still can’t get away from the fact that they’ve been sixth in the league for so long.
“Man United can’t be sixth, that’s why they brought Jose Mourinho in.”
Manchester United will now turn their attentions towards their Premier League home clash against Watford at Old Trafford next weekend.
The Red Devils are looking to break back into the top four this season after the disappointment of their fifth-placed finish under Louis van Gaal last term led to the Dutchman’s sacking.
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