The 30-year-old midfielder earned praise from Red Devils boss Sir Alex Ferguson for his spirited performance in the middle of the park, and hailed 'a big three points' to continue the club's revival and keep the pressure on leaders Manchester City.
"It was important we got the second goal, their keeper made some fantastic saves and we knew we needed the second to give us a cushion," Carrick told Sky Sports. "It's a big three points."
Asked if he had forgotten what that goalscoring feeling felt like, he added: "It's been a long time coming but it was an important goal and a big win for us."
United wasted numerous chances after taking the lead after less than a minute played, when Wayne Rooney converted a well-taken header to put the reigning champions in the driving seat.
"Their keeper made a lot of good saves but we're thankful for a 2-0 win, it's what we came here to do," added the striker.
"It was a great ball by Antonio [Valencia] and as a forward you try to put yourself in position and thankfully I got a good connection."