David Moyes' men overcame a 2-0 deficit from the first leg of their Champions League last-16 tie with the Greek champion after a hat trick from Robin van Persie, with Giggs also starting and playing a key role in the victory.
The 40-year-old admits he would enjoy a more prominent role in the United setup, having featured just 11 times in the Premier League this term.
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"I hope so, yeah, I have probably not played as much as I would like in the last few months but hopefully," the Welshman told reporters. "I think the team [against Olympiakos] had a mixture of a lot of things: pace, experience, power. That's what Manchester United is about and we showed that. We showed what we are capable of."
However, Giggs did warn that United's poor performances this season could lead to a long-term decline if the club is not careful.
"Well, you can see why people are saying that because we haven't produced it this season on a regular basis," Giggs 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. We showed it [on Wednesday] and we have to show it more consistently.
"We have just been not consistent enough. And not produced football like we have [against Olympiakos]. We are capable of it so that's the disappointment. I see every day in training what the lads are capable of and they have not transferred that into the games and we need to do that."