Head coach Franco Smith hailed Glasgow’s defence and problem-solving as the Warriors reached a maiden European final.
A powerful second-half display sank Scarlets 35-17, setting up a Challenge Cup final against Toulon or Benetton.
Glasgow trailed 14-7 at the break, but blew their opponents away with four converted tries thereafter, keeping the Welsh region at bay at the other end.
“Defence wins finals,” said Smith, whose side won the second half 28-3.
“Attack puts you in a position to win it, but it’s defence which ultimately wins you trophies.
“That is the most important thing for us as a collective. I felt the way we were defending was good enough. It took a really big effort from the guys.
“Solving problems in-game and on the field is something we’ve been working to all season. It’s something I’ve actually challenged the players on.
“Last week against Connacht, we had a couple of backs off and [back-row] Matt Fagerson playing centre.
“With things like that, you really need to understand the process of what you’re doing. Under pressure here, they had to work it out. That was the chat at half-time.”
Before the Dublin final on 19 May, Glasgow host Munster in the URC quarter-finals this Saturday.
Scotland and British and Irish Lions lock Richie Gray was a late withdrawal at Parc y Scarlets having been struggling with illness.
The 33-year-old was due to make his 100th Glasgow appearance, but Smith says he should feature against the Irish province, while praising the impact of replacement JP du Preez.
“That’s the best I’ve seen JP play,” he said of the 6ft 10ins South African.
“I’ve coached him with the Cheetahs, I’ve seen him play for Sale, and tonight he was fantastic, absolutely excellent in what he did.
“Richie will definitely be available for Munster. It wouldn’t have been the right thing to play him. Hopefully next week at home he gets a chance.
“Munster are lurking, so there’s still a lot of work for us to do this week.”