The holders were sent crashing out of the competition in dramatic style last night when their Irn-Bru First Division opponents claimed a last-gasp 3-2 win.
The cup exit came just a few days after Rangers had earned plenty of plaudits for their impressive Old Firm derby success on Sunday.
McCoist had told his players to forget about the triumph over Celtic and turn their focus to Falkirk, but he admits they never matched the efforts they demonstrated against their great rivals.
He said: “We told them the message, everybody knew the message.
“It doesn’t matter who the opponent is, if you don’t go out and play, if you don’t show them the respect by playing the game at a high tempo, then that can be a great leveller.
“We created a lot of chances and we didn’t take them, but the bottom line for me is that we didn’t play the game in the manner that we should have for an hour until we lost the goal.
“That’s why we are not in the cup. We will certainly have a look at it.
“We will definitely have a chat about it – of course we will. But we will just have to get a reaction at Dunfermline on Saturday. It’s as simple as that.”
Farid El Allagui grabbed a double for Falkirk, before Rangers hit back through late goals from Dorin Goian and Nikica Jelavic.
But, just as the third round tie appeared to be heading for extra-time, Mark Millar netted the winner deep into injury time to rule out any prospect of a domestic treble for the Scottish champions this season.
Millar, who signed for Falkirk from Celtic, hailed his winner as the highlight of his career so far.
He said: “This is the best thing that has happened to me so far. I want to play at the top level, whether it be with Falkirk or someone else, and I just want to kick on from here now.”