The Northern Ireland veteran is now on the books of Olympiakos and watched his team-mates inflict a 2-0 Champions League defeat on United last week in the first leg of a last-16 tie.
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Olympiakos' triumph caused a stir, yet Carroll, who made 68 starts for United in a four-year stint at Old Trafford between 2001 and 2005, insists he was far from surprised.
"[The win] was a shock for a lot of press people but the players knew themselves they had a chance," Carroll told Sky Sports.
"We watched a lot of Premier League games this season and knew United had not been performing. On the night when I was watching it live from the stands, I've never seen a Manchester United team like it.
"They've got good players but they had no hunger, no fight in the team so it was a shock in that way but not a shock the way we played. The goals we got were well deserved.
"At the end of the day you can be a good player but you have to give 100 per cent and give everything.
"For me Manchester United didn't give that and looked like they had no hunger and fight for the game.
"I don't know if they thought they would get an easy game but no professional should go into a football match and think that."
United will get a chance to atone for their below-par first-leg display when Olympiakos head to Old Trafford for the second leg on March 19.