Clermont had to produce a character-building final 10 minutes to resist Munster's late rally and finish as 16-10 winners of an absorbing semi-final clash in Montpellier.
Delighted with Clermont's progress to the Aviva Stadium final on Saturday, May 18, their Welsh back Byrne said: "It is a dream come true to finally reach a Heineken Cup final. It was the toughest game we've had all season and you've got to hold your hands up to Munster for that. They wore the famous red jersey with real pride."
He added: "We fully deserved to come through with the win. We had a few opportunities (to score a second try), but the ball didn't stick. We got a bit nervy, but hopefully we will come back stronger for the final.
"Whoever we face it will be another very tough challenge. We will do our homework and come out firing," he added, with Saracens and Toulon meeting in the second semi-final on Sunday at Twickenham.
Ronan O'Gara, the record points scorer and most-capped player in Heineken Cup history, would not be drawn afterwards on whether this was his final outing at this level.
The Munster out-half had kicked the visitors in to an early lead and it was his perfectly weighted grubber kick that teed up Hurley for the only try of the second half.
The raw emotion was etched on the 36-year-old's face after the final whistle as the Irish province bowed out at the penultimate stage.
"Defeat is extremely hard to take after you have put so much into a game like that. But it is winner takes all in a semi-final," said O'Gara.