The striker insists a strong European campaign is always a priority and believes David Moyes' side can go far in the competition.
David Moyes’ side faces Olympiakos in Greece in the first leg of their round-of-16 tie on Tuesday evening.
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"You always want to win," Rooney told reporters.
"One is never enough, especially at this club. You have to keep trying to get into those finals. The feeling you get when you win the trophy is incredible.
"There's no way you want to stop at one. You want to win every year. That's impossible, but if we can get to the final that will be great. It's an opportunity to win another trophy. Hopefully we can do that."
United topped Group A ahead of Real Sociedad, Shakhtar Donetsk and Bayer Leverkusen and Rooney feels achieving a positive result should be his side’s main focus in Athens.
"I think we have the quality to go really far," said the forward.
"The main aim is to get the right result on Tuesday and then take each game as it comes. The year Chelsea won it they nearly went out about three times.
"You just have to keep going, whether or not we get the right result or not. We're looking to get the victory and then progress to the quarterfinals."