Northampton boss Phil Dowson hailed his team's "courage" as they shocked Leinster to claim a first Investec Champions Cup final appearance since 2011.
Almost 20-point underdogs coming to Dublin to face a Leinster side who reached the last three finals, the Saints edged a 10-try shootout to leave Leo Cullen's men stunned as another European campaign came to a shuddering halt.
The English champions scored five tries and led for most of the game, with Tommy Freeman scoring a first-half hat-trick, however, they had to withstand a late surge by the hosts, who thought they had scored a try to win the contest after 79 minutes.
Even after that, Leinster had one final chance but got turned over on the line.
Dowson said they had studied Leinster's last two European games, in which they scored 114 points and conceded none.
"We learned a lot from the two knock-out games coming into this, in terms of Glasgow and Quins and how to attack that defence," the director of rugby told RTÉ Sport's Michael Corcoran.
"We've been working on our own game all season long and the belief inside was very strong. We talked about the belief we had in ourselves, regardless of what was said on the other side.
"I thought we finished the first half very well and started the second half very poorly, which gave them a huge amount of momentum and it was a rear guard effort after that.
"There's obviously things we can do better but the effort and intent that we had to work hard for each other was incredible."
Result: Leinster 34-37 Northampton
— RTÉ Sport (@RTEsport) May 3, 2025
Heartbreak for Leinster as they fail in the final play to breach the Northampton try line
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Replacement Ross Byrne touched down with one minute to go but after a lengthy TMO consultation, referee Pierre Brousset awarded a penalty to Leinster and sent Alex Coles to the sin-bin, but the Saints had one last defence stand in them.
"I thought we showed tremendous courage," he added.
"We trusted our defence and we just about got there.
"The heart and courage of the group together was outstanding.
"The thing that was going through my head was that if they score here, it feels cruel.
"I know sport's cruel and I know sport's unfair and that's the beauty of it but to be leading, I think we led the whole game, I don't know.
"To have lost it in the last minute with a bobbled ball and a referee's decision. Was it a knock on? Did Colesy [Alex Coles] release?
"It's all very intricate and subjective, and the referee makes a decision there and if we'd lost that I would have been gutted for the players because I know how hard they've worked, how much they've put into it. I see the lads at half-time blowing and I'm like, whoosh, that's a tough first 40 minutes.
"That's what was going through my head, it's so close and we concede here that doesn't feel quite right, and what do I say then to try and build them back up?
"Then as soon as we get [the turnover] I think Juarno [Augustus] took the ball off them on their tap and go, I just said to the coaches, we're going to Cardiff, and Sam Vesty broke my glasses."
Freeman's hat-trick took his season's tally to nine in Europe and ultimately saw the visitors over the line.
"We probably came in as the underdogs but the fight we showed, the squad we've got, we know we can do this performance," said the England wing.
"We know if we can get our game on the pitch we can take anyone on. They said Leinster [would win] by 30 but here we are.
"We put our game on the pitch, things start to happen, we stretch defences.
"Down to 13 we've got to show heart, we've got to show love for each other, and I thought we did that for 80 minutes and we got the result."
Northampton will play the winner's of Sunday's semi-final between champions Toulouse and Bordeaux in Cardiff on 24 May.
