Carrick says United have been unlucky several times during their 10-year wait for a win at Chelsea.
One notable occasion was in 2009 when United chief Alex Ferguson was furious with referee Martin Atkinson.
Carrick said: "Over the last three or four years we've had some really great performances there and not got what we deserved.
"So this time it was sweet to get the three points.
"We've really played some great stuff there and the performances have been spot-on.
So to come away with no wins has been disappointing. 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 it around for us. We'll take what we get.
"After not winning there for a long time against our biggest rivals, we wanted to put that right."