The Gers are 23 points in front of the Pars in SPFL League One - and have beaten them 3-1 and 4-0 in their two previous meetings in the 2013/14 campaign.
But McCoist knows that what happened in those matches will not matter when their fifth-round cup-tie kicks off at Ibrox tonight.
And he has urged his charges, who can still win an unprecedented domestic treble comprising League One, the Ramsdens Cup and the Scottish Cup, not to get complacent.
He said: "Dunfermline are in a good position. They've effectively got nothing to lose. Nobody expects them to win. They will come at us.
"We have beaten them twice in the league and are 23 points ahead of them in the table.
"But if we started looking at it that way it would extremely dangerous. So we won't be doing that.
"I think it eases the pressure to a certain degree on the Dunfermline boys and I think they'll be well up for it. You'd be staggered if Jim Jefferies hasn't got them raring to go.
"We have to earn the right to get into the quarter-finals. If we can win this one it obviously takes us a step nearer to winning it."
McCoist added: "Anybody can win a cup, absolutely anybody. I don't think there is any doubt that Celtic are the favourites to win it.
"There are strong teams in the top flight. At Aberdeen, Derek McInnes has done and is doing a fantastic job with them reaching the League Cup final.
"There are one or two teams I would still reckon would probably be a bit stronger than us in the top flight.
"That is not to say that we couldn't go on a good run and do well in the cup. That is the aim and the target."
Meanwhile, McCoist has taken a thinly-veiled swipe at the SPFL for deciding to stage the League Cup final between Aberdeen and Inverness Caley on March 16 at Celtic Park.
Parkhead will host the William Hill Scottish Cup final in May as Hampden is being redeveloped in preparation for the Commonwealth Games.
And it had been widely-anticipated by that Ibrox - which will host both of the Scottish Cup semi-finals - would be awarded the League Cup final.
McCoist is unimpressed with SPFL chief Neil Doncaster's rationale Ibrox would not be ready following Rangers' potentially crucial league clash with Dunfermline 24 hours earlier.
McCoist said: "Call me an old cynic, but I didn't fancy our chances of getting the final.
"I did say to Graham Wallace (the Rangers chief executive) that, if we were allowed to bet, which of course we're not, he should get a few quid on the final not being at Ibrox.
"Neil, or indeed, whoever is running the SPFL, made the decision. That's something they'll have to live with."