Jake's Montpellier to meet Quins in Final
But the Dragons, in their second successive semifinal, earned huge praise - despite the 12-22 loss - for their brave defensive display and actually outscored their hosts by two tries to one - with a strong fightback in the final quarter after falling 22 points behind after an hour of play.
The Top 14 club will now go on to face Harlequins in the Challenge Cup Final at Grand Stade de Lyon on Friday, 13 May.
It will be their first Final, while the Quins will be seeking to win their fourth title.
The Dragons went to Kingsholm and beat the reigning champions, Gloucester, in the quarterfinals, but this was a bridge to far for them against a side sitting second in the French league and boasting 11 wins in their last 12 matches.
Montpellier, coached by the South African World Cup winner Jake White, dominated the opening exchanges and enjoyed most of the territory and possession in a first-half spent softening up the brave Dragons defence. Even so, the visitors had the first chance to open the scoring, but Dorian Jones missed with a sixth minute penalty.
His opposite number, however, was in no mood to miss. Catrakilis hit the mark with four successive penalties in the first-half to give his side a 12-0 interval lead. The Dragons had the chance to shoot for goal with the last kick of the half, but Carl Meyer was wide this time.
Dragons coach Kingsley Jones admitted at half-time his side needed to sort out their scrum, which was wilting under the pressure of two Springbok World Cup winners in the Montpellier front row and a 42 stone second row pairing, but they continued to suffer at the set-piece in the second half.
A neat grubber kick to the home line by Meyer almost earned the Dragons a try in the opening few minutes of the second period, but that man Catrakilis added more points from his boot to stretch the lead to 15 points.
Then came the try that gave the Frenchmen an unassailable lead. Australian scrum half Nic White, on as a replacement, spotted some space in the Dragons 22 after a turn-over on half way and his pin-point kick earned his side a five metre line-out. Bismarck du Plessis found fellow Springbok Pierre Spies at the tail of the line and then joined the juggernaut to claim the try.
The Catrakilis conversion was a formality and that was the end of the home' side's scoring. The Dragons, though, weren't only just getting started. Meyer set up a try for Hallam Amos and then the full back crossed for a scored to ensure his side could leave the Altrad Stadium with their heads held high.
The scorers:
For Montpellier:
Try: B du Plessis
Con: Catrakilis
Pens: Catrakilis 4, Paillaugue
For Newport Gwent Dragons:
Tries: Amos, Meyer
Con: O'Brien
Teams:
Montpellier: 15 Benjamin Fall, 14 Timoci Nagusa, 13 Robert Ebersohn, 12 Frans Steyn, 11 Marvin O'Connor, 10 Demetri Catrakilis, 9 Benoît Paillaugue, 8 Pierre Spies, 7 Akapusi Qera, 6 Fulgence Ouedraogo, 5 Paul Willemse, 4 Robins Tchale Watchou, 3 Jannie Du Plessis, 2 Bismarck Du Plessis, 1 Mikheil Nariashvili.
Replacements: 16 Mickael Ivaldi, 17 Yvan Watremez, 18 Davit Kubriashvili, 19 Thibaut Privat, 20 Wiaan Liebenberg, 21 Nic White, 22 Benjamin Lucas, 23 Anthony Tuitavake.
Newport Gwent Dragons: 15 Carl Meyer, 14 Adam Hughes, 13 Tyler Morgan, 12 Adam Warren, 11 Hallam Amos, 10 Dorian Jones, 9 Sarel Pretorius, 8 Toby Faletau, 7 Nic Cudd, 6 Lewis Evans, 5 Nick Crosswell, 4 Rynard Landman, 3 Brok Harris, 2 Elliot Dee, 1 Phil Price.
Replacements: 16 Rhys Buckley, 17 Boris Stankovich, 18 Lloyd Fairbrother, 19 Matthew Screech, 20 Ed Jackson, 21 Charlie Davies, 22 Angus O'Brien, 23 Jack Dixon.
Referee: Wayne Barnes (England)
Assistant referees: JP Doyle (England), Greg Garner (England)
TMO: Rowan Kitt (England)
Source: @ERChallengeCup