The onus is on the Light Blues to hit back in the right manner after a hugely disappointing 3-0 loss to the Highlanders at Ibrox on Wednesday.
But the Third Division leaders will come up against last season’s champions at that level tomorrow and they have taken their good form from 2011/12 into this term.
The Wasps currently lie second in the Second Division as they go for back-to-back promotions having won six of their 10 league outings so far.
They were 5-1 victors in their most recent game against Albion Rovers and they are continuing to do well under Paul Hartley.
McCoist knows the Recreation Park team will come to Glasgow feeling they can get a positive result.
And from that point of view, he knows it will be tougher than some might imagine as his men seek to progress into round four.
McCoist said: “It’s a game against a team from the lower leagues who plays as good a game of football as any other team in the lower leagues.
“They had a great year last year and they’re having another great one this year, sitting second top just now.
“They scored five goals last week and as a team and a club in a rich vein of form, they’re full of confidence and they’ll be extremely dangerous opponents.
“I know the Alloa boys will be dying to put on over on us. They’ll be looking up on this as being a good time to play Rangers after the game in midweek.
“They will be reasonably fresh and I think they are going away together tonight as a group to prepare.
“That said, it’s a home game in the cup against another team from a similar league and situation to us. In that respect, we should be very hopeful we can go out and get a result.
“It’s probably a game where if we win, we won’t get too many pats on the back and if we lose we’ll get a bit of stick.
“I hope we win the game and we’re not getting too many pats on the back. That’s a far better option for me.”