Carrick felt that his side should have beaten the Blues at Stamford Bridge.
United came back from three goals down to draw.
Carrick told MUTV: “We were slightly disappointed in the end.
“Obviously, when you’re 3-0 down and have your backs against the wall, if someone offers you a point then you’ll be happy with that but getting a third goal with a fair bit of the game to go, we fancied ourselves to go on and win it.
“We probably looked like the likelier team to do it. They had a good free-kick but it’s a strange feeling in many ways, it was an up and down afternoon and in the end, a point is a point and we can take an awful lot from that game.
“We played well in the first half and created some opportunities. Even when we were 1-0 down at half-time we were a bit stunned and surprised but that’s how it was and we had to deal with it.”
“I think other teams who were watching that and seeing us go 3-0 down, they would have been thinking what a good afternoon it has been for them,” he added.
“Then for us to come back in the manner we did might give them a little dent and a boost for us.”
