Twelve months after they were humbled by the Doonhamers at Ibrox, the Light Blues got their revenge at Palmerston as goals from Bilel Mohnsi, Jon Daly and Lee McCulloch clinched a key win.
The Gers join Annan Athletic, Stenhousemuir and Raith Rovers in tomorrow's last-four draw and McCoist is determined to go all the way this season.
He said: "It would be great to win it. We want to win every trophy we are in. We were disappointed last year to get knocked out by the team that we beat tonight. The one I want to win is the league, I won't be in a job if we don't get promoted and win the league.
"Everything else we enter we want to win. We want to win both cups, the Scottish and the Ramsdens."
Just days after seeing his side hit Arbroath for five on SPFL League One duty, McCoist's side again found their form in the final third as they continued their terrific scoring run this season.
The centre-back pairing of Mohnsi and McCulloch has now chipped in with six goals in two games and McCoist is delighted with their superb showings as both ends of the field.
He said: "Lee has been terrific as you know and we always felt that if we could get Bilel signed he would be great for the team.
"They look as though they have got a partnership forming, which is great.
"The experience of the two full-backs, Fozzy (Richard Foster) and Lee (Wallace), helps.
"We had a problem defending set plays last year, we didn't have a lot of height.
"I am not going to say for a minute that we have solved that problem but we certainly look a bit better."
Despite Mohnsi and McCulloch seemingly forming an impressive partnership at the heart of the Rangers rearguard, McCoist is keen to bring in another defender to bolster his Ibrox ranks.
The Gers have offered a contract to former Hearts star Marius Zaliukas after he showed up well during a trial period at Murray Park and McCoist hopes there will be movement sooner rather than later as he targets his 10th signing of the campaign.
The Ranger manager said: "There is a contract offer that has been put to Marius and hopefully we will hear back from him soon.
"I am quite relaxed about it. I don't really want to put any pressure on him.
"I would hopefully be speaking to him in the next two or three days just to see if there is an update."