The England striker played a pivotal role in helping United secure Premier League football for another season by beating Tottenham Hotspur 2-0 at Upton Park this afternoon.
Although not on the scoresheet, Carroll proved a constant menace to the Spurs back four, and the 25-year-old hailed the "great" Allardyce for supporting him through times of injury trouble.
He told BBC Sport: "I've had a tough season getting fit and staying fit but I am feeling strong now.
"Sam Allardyce is a great manager. He has trusted me and played me when I've not been 100% fit.
"He has a lot of faith in me, I respect that and have to give it my all when I go out on to the pitch. His man-management of me has been great."
Harry Kane deflected a Carroll header into his own net for the opening goal before a Stewart Downing free kick doubled the advantage over 10-man Tottenham, who had defender Younes Kaboul sent off.
Carroll is among those expected to be considered by England manager Roy Hodgson for a place in his 23-man squad for the Three Lions' World Cup campaign in Brazil next month.