In the build up to the tie with their League One counterparts, McCoist suggested Rangers could hold their own with the top sides in Scotland.
But after guiding a team to the last eight of a major domestic competition for the first time, McCoist reckons Rangers will have to replicate their performance against the Pars to progress to a semi-final at Ibrox.
McCoist said: "I would be happy if we could replicate that type of performance in the next round against anybody. I thought for the majority of the game we were really good tonight.
"I have no preference for the draw for the next round other than a home tie.
"Can we beat anyone left in this competition? I don't know, I really don't know. That level of performance I would be happy with playing anyone.
"I'm not going to say we would beat anybody because one or two teams - and obviously Celtic - would be favourites.
"There are a lot of good teams left in the competition but if we put in a performance like that then I would be happy to take my chances against most teams - but that is not to say we would win."
Dunfermline counterpart Jim Jefferies reckons his team lacked their usual fighting spirit as they lost 4-0 to their opponents for a second-successive occasion this season.
Jefferies said: "The last two times we played them, Rangers were complaining about us being physical. But we never laid a finger on them tonight.
"If they didn't like what we gave them last time, we should have given them more of it and then we might have had a better chance.
"When you don't compete against a side like that it makes it very tough."