Goals from full-back Rafael da Silva and veteran midfielder Ryan Giggs sealed the points for United at Loftus Road, which in turn saw them open up a 15-point advantage at the top of the Premier League table.
Despite Carrick's admission that United's performance wasn't "pretty", the 31-year-old insisted that he was happy to have won the match.
"We expected a tough game and we certainly got it, especailly in the first half," Carrick told MUTV. "The pitch was bouncy and bobbly and it's tight at the best of times here [at Loftus Road].
"It was just a case of adapting to the conditions and the context of the game, battling it out at times. I thought we did that well.
"Sometimes you have to do that. Throughout the season it's not always going to be pretty. Sometimes you have to grind out results, work hard and make the most of your opportunities."
Next up for United is a league clash against Norwich City at Old Trafford on Saturday.