Rooney, who signed a new five-and-a-half-year contract earlier this week, tasted glory in the competition with United in 2008, before finishing on the losing side in the final against Barcelona in 2009 and 2011.
United have not looked like potential European champions this season, falling 15 points off the pace in the Premier League and crashing out of both domestic cup competitions, but Rooney says that their objectives remain the same.
"You always want to win it," he said on Monday, on the eve of the first leg of United's last 16 tie away to Greek champions Olympiakos in Piraeus.
"To win one is never enough, especially at this club. You need to keep trying to get into finals.
"The feeling you get when you actually win the trophy is incredible, so there's no way you want to stop at one. You want to win every year. Obviously that's impossible, but if we can go to the final, it'd be great for us. It's an opportunity to win another trophy, so hopefully we can do that."
Barcelona and defending champions Bayern Munich have already produced shows of strength in the tournament with 2-0 first-leg wins over Manchester City and Arsenal in their respective last 16 ties.
However, rather than being daunted by the sight of United's domestic rivals coming unstuck, Rooney says it has only whetted his appetite for the competition.
"They've been brilliant (games) to watch," he told a press conference. You see Barcelona against Manchester City. FC Barcelona were incredible and keep the ball really well.
"Then you watch Bayern Munich and it's almost the perfect performance at Arsenal. I know both teams (City and Arsenal) were down to 10 men, but the way they keep the ball and open teams up is great to watch.
"We have to try to do that, try and keep the ball, be patient and break teams down. A lot of the teams we're playing are sitting back with all the team, so it's down to us to move the ball quickly and break them down."
United centre-backs Phil Jones and Jonny Evans have not travelled to Greece due to injury and record signing Juan Mata is cup-tied, but manager David Moyes has an otherwise strong squad to select from.
United will start as favourites against a team who last reached the quarter-finals in 1999, but with Olympiakos having pipped Benfica to a place in the knockout phase, Moyes says that they must be respected.
"Olympiakos have done very well against Paris Saint-Germain in the games I've watched, and Benfica," he said.
"They came through in a difficult group, they've got a great home record here, so we know it's a difficult night. They've a big support. It's a tough game."
With United 11 points adrift of Liverpool in the race for a top-four place in the league, they may need to win the Champions League to qualify for next season's competition, but Rooney believes that the Olympiakos tie can act as a springboard to a successful run-in.
"As a group of players we have to take responsibility for our league position," said the 28-year-old England striker.
"We know we're better than that and we haven't performed as well as we know we can do. We know that and as a team it hurts when you know you can do better.
"It's important that we finish the season strongly and take that momentum into next year, but more importantly we try and get into that fourth spot and try and do well in the Champions League. It's important to us all."