Benitez said Liverpool must win its nine remaining games and hope United drops at least several games. The win at Old Trafford moved Liverpool to within four points of United, which still has a game in hand.
"It depends on United because they have to lose some games and we have to win everything," said Benitez. "We have more belief, more confidence and we have to get three points in every game and see what happens to them. We're more optimistic than we were before the game but we're still realistic. Clearly, it will be difficult but we can do it."
Liverpool came from a goal down on Cristiano Ronaldo's penalty kick to defeat United. Fernando Torres, Steven Gerrard, Fabio Aurelio and Andrea Dossena scored for Liverpool.
Manchester United manager Sir Alex Ferguson said his club was happy to be where it is.
"If the league was starting today," he said, "we would [happily] take a four-point lead, and we've also got a five-goal advantage on goal difference."