The Reds edged a game shrouded in controversy as Chicharito turned in a late winner against the nine-man hosts, but the midfielder cared not a jot as the Blues' lead at the top of the Barclays Premier League was trimmed to one point.
"It's a huge three points," Carrick told MUTV. "Not winning here for a long time against our biggest rivals, we wanted to put that right and we wanted to win for that.
"Plus the fact that if we had lost today we would've been well adrift. I know there's a long way to go, but it wouldn't have been a good position for us to be in. So for those two reasons it was a big result.
"Over the last three or four years we've had some really great performances here and not come away with what we deserved, so today it was sweet to get the three points.
"We've really played some great stuff and the performances have been spot on, so to come away with no wins has been disappointing and we felt the next win was close. We have had some decisions not go our way and it's been tough for us here, but maybe that turned around for us today. We'll take what we get!"
Chelsea, United and Manchester City are now separated by a single point at the head of the table and, buoyed by the Reds' impressive form at imposing venues this term, Carrick insists it is key to keep winning such headline-grabbing encounters.
"Especially against your rivals – the likes of Liverpool and Chelsea, Arsenal next week – it's important you take points off them," said the