United captain Rooney was on target at Old Trafford as Louis van Gaal's side won their sixth successive league match.
After a slow start to the 2014-15 campaign, United have consolidated third spot in the standings, eight points adrift of league leaders Chelsea.
While the gap is relatively substantial, given Chelsea's dominance after 16 matches, Rooney has not given up hope of lifting the Premier League title for a sixth time.
"I think we have to believe that we can win the title," Rooney said. "We are eight points behind and coming into a busy period.
"If we can win our games and the others have one bad result then there's nothing in it. We have a lot of new players but we have been here before and this is where the experience of myself, Michael Carrick and Darren Fletcher can rub off on the other players.
"We have to keep winning our games, hopefully get back to the top and then you never know. We have shown a great resilience.
"Some of the games haven't gone the way we would have liked but we are winning them and that is a great quality to have."
Rooney, who has scored six league goals this season, added: "We won the league two years ago and we weren't great in a lot of those games but we got the results. Sometimes you have to do that.
"I have seen Chelsea a couple of times this season when they have not played great but have nicked a win as well. We need to try to get the performances right and, if we do that, then we are confident we will win the games."
United are away from home on Saturday, travelling to Villa Park to play Aston Villa.
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