Man United produced a fantastic performance during the game and sealed a crucial win thanks to a memorable brace from Juan Mata.
The result left Man United fourth in the Premier League, five points ahead of Liverpool in fifth.
Carrick hailed his teammates following the victory and said it gives them a platform to build on in the race to finish in the top four.
Speaking about the result, Carrick said: ”It’s a massive one for us. It was built up, we’re so close in the table. It’s three points and we’re delighted in the win.
“In the first half we played well, in the second half not so good. We were probably better against 11 players. It was chaotic out there, 100 miles per hour, and lots of mistakes.”
On top of the result, a sending off for Liverpool’s Steven Gerrard provided icing on the cake for United fans.
Lasting just 38 seconds after coming on as a half-time substitute, Gerrard received his marching orders after stamping on Ander Herrera. After his infamous slip against Chelsea last season, the episode topped off a fantastic afternoon as far as United were concerned.