United had not win a Premier League game at Stamford Bridge in over a decade before this weekend's contentious victory, and Carrick believes the win has set his side up well in the fight to top the table.
"Against your rivals - the likes of Liverpool and Chelsea, Arsenal next week - it's important you take points off them," Carrick told MUTV.
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"That's why it was important and next week is just as important. It's a good start to the season. We've obviously had a couple of defeats but we've bounced back and we're still in a good position, so we can be happy.
"It's a huge three points. Not winning here for a long time against our biggest rivals, we wanted to put that right and we wanted to win for that.
"Over the last three or four years we've had some really great performances here and not come away with what we deserved, so 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. We'll take what we get."