United opened the scoring on 23 minutes when Rafael ran onto a bouncing ball and sent a thunderous shot screaming into the top corner from 20 yards.
"A goal like that from Rafa put us in a great position," Carrick said. "I was right next to it. It was an unbelievable strike. It caught me by surprise, to be honest. Probably like everybody else!"
A second-half strike from Giggs made sure of the win, while at the other end of the pitch United kept a third successive clean sheet. At the heart of the Reds' defence was the formidable pairing of Rio Ferdinand and Nemanja Vidic, a factor Carrick believes was vital in helping to secure the three points.
"You know what you're going to get [with Rio and Nemanja]. They know each other's games inside out, and with me in front you have that little triangle that we use to try and defend well and start counter-attacks from.
"It was a case today of doing the basics right and letting the front boys produce the quality. As it turned out it was Rafa who produced the quality! It could have been more in the end but we'll take what we got."