Carrick could have been playing for Magpies if Kevin Keegan hadn't disbanded Newcastle's reserve team during his first spell in charge at St James' Park.
The England midfielder, 26, said: "It's the first time I've actually won here so it was very satisfying. It's a great final score. Normally I come back and it hasn't been that good for me. But this is a really good day because we've closed the gap.
"We knew beforehand this was a big three points for us. With Arsenal just getting a point, it's a great day. Now I can enjoy my weekend and catch up with a few friends and family.
"Coming here and seeing them in the stands and playing like that's a great feeling."
Carrick may not feel so great if he is dumped on the bench again at Fulham next week - but he knows that is why United are looking so strong.
Their squad is in great shape as they chase glory on three fronts and boss Ferguson can afford to keep everyone fresh.
The former Spurs star added: "Obviously you want to play every week but it's the best club in the world and you're going to have top players in every position. We're all competing but in a friendly way and it brings out the best in everyone. We're all raring to go.
"There were changes again from the other night, I'm sure there'll be changes for the next one and it's working well at the moment. Maybe we were a bit too comfortable because we didn't play great in the second half but when they scored we put the game to bed."