Queens dumped the Light Blues out of the competition last season, thanks a dramatic penalty shoot-out victory at Ibrox, before going on to win the trophy.
McCoist admits the defeat still hurts and, while payback is not the motivating factor, he is keen to make amends for what was one of the poorer results of last term.
He said: "It certainly hurts us. Queen of the South knocked us out and deservedly so. At the same time, we felt their second goal was offside and to get beat on penalties is sore at any level.
"They went on to win the cup and deserved to do so. It definitely hurt us. I never use the word revenge, I don't like the word revenge.
"But this game gives us an opportunity to go down there and reach the semi-finals of the tournament which is our aim."
Rangers head into the quarter-final tie at Palmerston boosted by a 5-1 win over Arbroath at the weekend, with Lee McCulloch again stealing the show.
Despite playing in defence on Saturday, the skipper bagged a hat-trick for the second game in a row and McCoist had nothing but positive words for him.
He said: "We've still been talking about it and I can't remember the last centre-half to score a hat-trick.
"What's interesting as well is that it's six goals; five headers and one 30-yard screamer and no penalties.
"Every one of them has been absolutely top class. Nothing less than two goals from him tomorrow night will be acceptable I would have thought!
"He's in a great vein of form and he's a breath of fresh air to work with. At no time does he say he would rather play here or there.
"He just wants to play, he just wants a jersey and he will take any jersey.
"He's a throw-back to the old days and his type are maybe not a dying breed but there's certainly not as many of them about as there used to be. He's a great skipper."
The on-field action continues to play out against the backdrop of a bitter boardroom battle behind the scenes, which is set to come to a head at an annual general meeting next month.
But McCoist believes the club is moving in the right direction on the park despite the off-field issues.
He said: "From a football point of view, we are quietly pleased with the way things are going at the moment. It was a big disappointment in the League Cup but the most important thing in our progression and development is continuing to get out of the divisions that we're in.
"In terms of the harmony within the football club and the staff, I would hope it would be very good. Of course, like any workforce, you have ups and downs and disagreements and all that kind of stuff.
"But I think the team winning does create a better atmosphere within the club and it's better than it has been."
Meanwhile, the club's official website has confirmed a deal has been offered to former Hearts skipper Marius Zaliukas. The defender has been training with Rangers and is now back in his native Lithuania considering the offer.
McCoist told www.rangers.co.uk: "Marius trained very well with us and I know Craig [Mather, chief executive] had a chat with the board and myself, then put an offer to him.
"He has now gone back home to contemplate it and to have a think so hopefully we will hear from him soon.
"We as staff feel we should strengthen in the centre of defence although when you're getting hat-tricks from one of your centre-halves it's always encouraging and pleasing.
"I just feel we need to think about the longer term and it's an area we definitely need to bring someone in."