The Ulsterman’s 44th minute strike booked the Light Blues a place in tomorrow’s draw at Hampden.
And although Rangers can, and will, play better than they did tonight as the season progresses there were plenty of highlights for McCoist to focus on in his post-match interviews.
Chris Hegarty looked assured on his competitive debut as did Brazilian centre back Emilson Cribari who made his first start having recently joined the club.
On top of that youngsters Barrie McKay, Lewis Macleod, Kal Naismith and Robbie Crawford, a late substitute for Hegarty, all got first team action under their belts.
But being a former striker McCoist, not surprisingly, heaped praise on the matchwinner Little who put in a great shift.
He said: “It was a good goal we scored tonight, McCulloch did well winning a brave header in the middle of the park and Andy is very direct.
“The first thing he wants to do when he gets the ball is get a shot in and that’s what he does.
“He is always in the thick of the action, scoring goals, taking chances and missing chances.
“He’s all action and I’m delighted for Andy again.
“As for Emilson he came through the game well, you always wonder how players will cope coming to places where the tempo of the game is high.
“I thought he handled it well and I was very, very pleased with him.
“But overall I’m pleased to get through, it was a tough game.
“That wasn’t a shock, it was our third away game now and they’ve all been equally difficult.
“Brechin, Peterhead and here tonight, no surprises at all.
“But I thought we just about shaded it and deserved to go through, albeit Falkirk knocked the ball about well tonight.”
