While at Everton, Moyes failed to win any of his Merseyside derbies at Anfield, despite being in charge of the Toffees for 11 years.
However, as he prepares for his first outing against Liverpool as United manager, Moyes has defended that record.
"At Everton we couldn't compete with Liverpool's budget, so it was a case of hanging on to their shirt tails," he told the Daily Star.
"And in the last couple of years we were able to overtake them, when we finished above them in the league."
Moyes, who has won one and drawn one from his first two league matches as United manager, also said that he wants to improve his Anfield record and likened today's match to last weekend's encounter with Chelsea.
He added: "I would love to have a better record at Anfield and I will be doing my best to address that in this match.
"I go there this time with a different set of players – and the players I am taking this time are the champions of England.
"The same sort of questions were being asked about my record against Chelsea, before we played them last Monday."
Today's match kicks off at 1.30pm.