David Luiz’s own goal and Robin van Persie’s seventh league goal of the season gave United a perfect start, but the visitors were pegged back by goals from Juan Mata and Ramires either side of half-time.
However, Branislav Ivanovic and Fernando Torres were both sent off to swing the match back in United’s favour, with Javier Hernández scoring the winning goal in controversial circumstances.
Carrick felt United had to win to keep pace with Roberto Di Matteo’s high-flying side, and the England international believes it was a deserved win after previous disappointing results at Stamford Bridge.
“It’s a huge three points,” Carrick told United’s website. “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 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!”
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