But the French club, boasting players from nine different countries in their side, held on to make up for their bitter disappointment in losing to Leinster Rugby in last season's semi-final.
"It is a dream come true for me to finally reach a Heineken Cup final," said the former Ospreys star. "But you can't take anything away from Munster - they wore their famous red jersey with real pride.
"It was the toughest game we have had all season and you've got to hold your hands up to Munster for that. We had a few opportunities, but the ball didn't stick.
"We got a bit nervy, but hopefully we will come back stronger for the final. Whoever we face we will do out homework and come out firing."
Byrne will be hoping to become only the ninth Welshman to take home a Heineken Cup winners medal in Dublin on Saturday, 18 May, and follow in the footsteps of Tony Rees (Brive, 1996), Ieuan Evans, Nathan Thomas, Richard Webster (Bath, 1997), Andy Newman, Allan Bateman (Northampton Saints, 2000), Rob Howley (London Wasps, 2004) and Gareth Thomas (Toulouse, 2005).