The 19-year-old forward made the most of his first-team bow when he came off the bench to grab the clincher in a 2-0 win against Dunfermline on Saturday, after Steven Smith had opened the scoring at Ibrox.
The Light Blues are now under pressure to dispose of the Wee Rovers at the second attempt and book a last-four meeting with Dundee United in the Scottish Cup, after being heavily criticised for their efforts in the initial 1-1 draw.
The stakes may be high but, having had a taste of success already, Gallagher would love to be involved in the crucial clash.
He said: "You would have to ask the manager but I would like to think I've maybe put myself in with a shout. I'm just happy to be around the first team."
Asked what was going through his mind when he was pitched into the action for the last 15 minutes against the Pars, he admitted: "There was a combination of panic and joy.
"I had tunnel vision and was wide-eyed but I was just really pleased to make my debut. I'm just elated.
"I've been on the bench a couple of times but that was my first time on the pitch for the first team so it was a good feeling.
"I think it's everyone's dream to score on their debut. The ball just dropped to me and I hit it. It could have gone anywhere but I was lucky it went in the net.
"Any impact you can make in the first team is good so I was pleased to do that.
"It was a complete surprise to get on. I've been involved with the first team in training and in squads a bit more recently, so it was maybe building up to it, but I still wasn't expecting it."
The importance of the impending cup tie was reflected in McCoist's decision to rest key personnel for the visit of Dunfermline, having already wrapped up the Scottish League One title against Airdrie a few days earlier.
Jon Daly and Lee Wallace were named on the bench and Nicky Law was absent from the squad, while Bilel Mohsni was subbed at half-time and skipper Lee McCulloch was withdrawn after an hour.
McCoist said: "We had to get the balance right because we wanted to win the game and continue the good form and good results the boys have had in the league this year. It was important to keep the momentum going.
"At the same time, we know the game on Monday is a massive game for everybody at the club.
"It's an opportunity to get back here for a semi-final and we want that to happen so we had a bit of an eye on Monday's game."
With back-to-back league wins since that shock draw with the Coatbridge men, McCoist feels his side are in ideal shape for the re-match.
He added: "We've had five goals and a couple of clean sheets so we are going into the game in a very positive frame of mind.
"I don't think it did the likes of big Jon, Lee or Nicky any harm having a rest. We are doing everything we can to prepare for the job on Monday."
- Sports & Recreation