Wayne Rooney has called on Manchester United to remember the high-intensity attacking football that is the club's "DNA" to ensure a successful end to the season.

United secured their passage into Friday's Champions League quarter-final draw with a 3-0 victory over Olympiakos on Wednesday night courtesy of a Robin van Persie hat-trick, although the Dutchman's second-half injury has given his manager, David Moyes, cause for concern. Rooney, however, insists the team have to produce similar performances on a consistent basis if they are to salvage anything from a bitterly disappointing campaign.

"We have to. That's been part of our DNA over the years I've been here – that intensity, that running off the ball, the pace we play at," the striker said. "It's a big part of the way we play and it showed that when we do that to teams it's difficult for them to stop us. I think we're spurred [on] by the way the games and results have gone. It's not necessarily the comments which people have made, it's more the fact that we're not getting the results and as a team it's hard to take so we've kept working and hopefully it'll get better.

"It was a good performance. I think the performance and the result were much needed. It was a massive game for us. We came out with a great attitude and fully deserved the victory.

"After the first game in Athens and especially what happened on Sunday [losing 3-0 to Liverpool at Old Trafford], we knew that we had to come and give a big performance, for ourselves really – for our own personal pride and [for] the manager, and we've done that. I've said before our performances this season haven't been good enough and we owe the manager a big performance, but we know as players we are better than what we've done this season.

"As a group we have to show that and put it right. It's something we have to kick on from now. We've still got a few games left in the season and we want to build on this. Hopefully we can do that."

United are 18 points behind the Premier League leaders, Chelsea, and 12 from a Champions League berth, with nine matches left. Rooney believes the departure of Sir Alex Ferguson in the summer is a key factor in the disappointing season. "It was always going to be tough when Sir Alex left," he said. "It was obviously a massive change so we knew it was going to be tough but we didn't expect it to be as tough as it has been. But we have to put that right. We have to keep working, keep believing in ourselves and hopefully it'll get better."

He also backed Moyes's claim that despite being firm underdogs United could yet win the Champions League, much as Chelsea did in 2012 and Liverpool in 2005. "Yeah. In cup football anything can happen. With a bit of luck hopefully we can go far," said Rooney.

Ryan Giggs, who was inspirational against the Greeks in his first start for two months, downplayed any suggestion United could be facing the end of their era of domination, like Liverpool in the early 1990s. "Well, you can see why people are saying that because we haven't produced it this season on a regular basis," the Welshman said. "I know from experience what these players are capable of and a lot of them have been written off. I think there is a lot of quality within the dressing room."

Giggs also admitted he wanted to feature more. "I hope so, yeah, I have probably not played as much as I would like in the last few months," he said.

Van Persie's three goals took him to 14 in 23 United matches this season, and Moyes will not want to lose his services. He was carried off on a stretcher against Olympiakos and United should find out the extent of his knee injury on Friday. They face a tough trip to West Ham on Saturday before entertaining Manchester City on Tuesday evening.

After a virtually injury-free season last year, Van Persie has again been plagued in the current campaign as he was for most of his Arsenal career, the final year apart. A muscle injury in Japan on United's summer tour was followed by issues with his toes and groin once the season started and a thigh problem in mid-December that ruled him out for six weeks.