Falkirk beat Cowdenbeath 4-0 on Saturday in the Championship and McCoist has warned his team to take notice of the comments coming out of their opponents' camp ahead of the fourth-round trip.
McCoist told Rangers TV: "I'm already reading comments after Falkirk's good victory at the weekend - quite rightly - from one or two of their lads.
"They knocked us out of the League Cup a couple of seasons ago and are doing well in the league just now.
"They are looking forward to the Rangers game and they're looking to put one over on us again. You'd absolutely expect them to say that.
"If there was ever any doubt about how up for the game Falkirk are, you just have to look at their quotes in the newspapers. They're full of confidence.
"We've had them watched and they beat Livingston 4-1 recently, so it's a tough game for us this weekend."
McCoist's top-flight team lost at the Falkirk Stadium in their last season before liquidation, although Rangers gained revenge in both the League Cup and Ramsdens Cup last season.
And McCoist has warned that teams are just as determined to cause an upset against his side as they were before the club's financial collapse.
"We're a massive scalp, of course we are," McCoist said. "I make no apologies for saying the vast majority of teams raise their performance levels against us.
"That's not a criticism of them, it's just a statement of fact and it's totally understandable that they do that.
"We might not be the same team we were in terms of playing well in the Champions League and winning top-flight titles.
"But we are, without doubt, the same club and that's as big a thing for our opponents as it was before."
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