United kept a rare cleansheet in last night's 1-0 win over West Ham United.
Carrick told MUTV: "It has been a while since we got the first goal in a game.
"We had a spell, about a year or two ago, when we were starting games really well and killing teams off really early. We want to get back to that because Old Trafford is a difficult place to play when you go a goal down.
"We want to make it that way, certainly in the games that are to come because going a goal down has made things a lot harder for us than they should have been."