Franco Smith said Glasgow’s first appearance in a European final “means a lot” after they saw off Challenge Cup rivals the Scarlets 35-17 in Llanelli.
The Warriors will tackle Toulon or Benetton in Dublin on May 19, and they are the first Scottish team to reach the Challenge Cup final since Edinburgh did so eight years ago.
And they were good value for their semi-final triumph, scoring tries from centre Stafford McDowall, who claimed a double, scrum-half George Horne, flanker Rory Darge and replacement hooker Johnny Matthews.
Horne also kicked five conversions for a 15-point tally as the Scarlets were overhauled after leading 17-14 early in the second period.
“It means a lot to them. Everyone is very excited around that,” Glasgow head coach Smith said.
“But we know there are still a lot of learnings to take from this, a lot of improvement to be made. We have the ability, we have the skillset – we just need to now use the lessons learnt from this week better.
“The talk at half-time was about settling down. Even some of our internationals were just a little bit too nervous, which shows what this means to them.
“They didn’t want to lose tonight, and I thought we started off so well, but we got a little bit jittery.
“We calmed it down at half-time. The plan didn’t change. The plan was specific for this week and I thought we stuck to that even though Scarlets did extremely well to unsettle us and rattle us.
“Their line-speed from a defence perspective was very good, and we didn’t manage to get out of our half for various reasons, but it was important to show some resilience before the end.
“It’s about managing the emotional intelligence during the game and going into the next big challenge.”
While Glasgow now prepare for a United Rugby Championship play-off clash against Munster next weekend, the Scarlets’ season is over.
Wing Steff Evans claimed their solitary touchdown, with fly-half Sam Costelow landing four penalties, but a 13,000 crowd – the Scarlets’ biggest home attendance for five years – could not roar their team home.
Scarlets head coach Dwayne Peel said: “I thought at half-time it was an even contest and we were right in it.
“We just didn’t manage to get over the line in their 22. They held us out, and we shifted the ball to the edge but got bundled into touch twice, which is disappointing.
“I can’t fault the effort of our boys. I thought we were right in the game.
“We had three head injury assessments in the first 20 minutes, which is unheard of really. To lose all three, and then to lose Vaea Fifita as well is difficult.
“I think that definitely hurt us later on in the game, because they were bringing on fresh bodies and we didn’t manage to get the fresh legs on.
“But in saying that, I thought they did a job in the areas we thought. They were strong in set-piece and they managed to grind that one out in that respect.”