Carrick scored a late winner to secure a 2-1 victory away to Wigan as United are now just one point away from the Premier League title.
He told Sky Sports: “To score a goal as important as that is a great feeling. I had to make up for my miss in the first half. The win was vital tonight.
“Wigan didn’t sit back and defend, they came at us and caused us a few problems. They had a number of chances and we rode our luck a bit.
“It’s not the first time we’ve come from behind and we do it the hard way, but it’s a good feeling when it happens.
“Carlos coming on and scoring like that got us back in the game and from then on we just wanted to nick the winner and we’ve done that.”