The hosts picked a young team for the last-eight encounter against a Scarlets side packed with international talent and Mola admitted he was delighted with the desire shown by the Pool 5 winners.
"I'm very proud of my players and that's becoming a regular thing now. We'll really savour this victory," said Mola, after five Riaan Swanepoel penalties saw them through to a first European semi-final since 2005.
"Rugby belongs to the players and they all did a great job against the Scarlets. I feel honoured to be their coach, particularly as we made lots of changes to the team. We played with two 19-year-olds and we really faced up to a Scarlets team with lots of international players on the pitch.
"It's incredibly positive to start with youngsters in a game as big as this one. This summer we are going to lose some players to other clubs but we have shown that we have some good young players coming through. The future maybe isn't as bad for Brive as some people think.
"The team did everything they possibly could to stay in this competition and massive congratulations must go to all of them. We will keep fighting and fighting in the Amlin Challenge Cup and we'll hope to make the final now we're in the last four."
Brive will now travel to the Parc des Sports Aguillera in just under three weeks' time as they look to take another step closer to their first Amlin Challenge Cup crown.
The 1997 Heineken Cup winners have appeared in 10 Amlin quarter-finals and two semi-finals but have yet to make it all the way through to the season's showpiece.
Travelling to a side that can boast the likes of Dimitri Yachvili and Imanol Harinordoquy in the ranks would be a tough test for any side and, with fellow Top 14 giants Toulon and Stade Francais also still in the hunt for Challenge Cup glory, Mola knows Brive will start as heavy underdogs.
"There are now four French teams in the semi-finals - three big teams with a lot of stars and then Brive, after we caused an upset," added Mola.
"Biarritz are used to playing big European games. They were in the Heineken Cup Final just two years ago. We definitely won't start as favourites but we will go there with confidence and a lot of courage.
"Playing against Biarritz in the Amlin will be a different type of game to playing them in the Top 14. It will be a knockout game with a different style of refereeing as well. In this competition, you seem to be able to play through more phases and the rugby is therefore better to watch.
"I'm so happy for this team and now I'm hopeful we can keep on going."