Injury-hit Wasps started with six - and finished with eight - players aged 21 and under and Young believes they are the future of the club, currently battling against relegation from the Aviva Premiership.
Wasps, looking down and out when they trailed 23-9 after 60 minutes, hit back to level the scores at 23-23 before Dimitri Yachvili settled the issue with his sixth successful kick from as many attempts.
Director of rugby Young said: "At one stage we looked dead and buried but the players showed a lot of determination and a lot of guts to pull themselves back into that game. With eight minutes to go it could have gone either way.
"I don't think we were the better team and I don't think we deserved to win - but we could have won.
"They had that little more firepower than us and they were a bit more clinical when they had the chances.
"We were lucky to still be in the game at some stages but I was really proud of the youngsters who gave everything. They showed a lot of character.
"The performances of Joe Launchbury and Sam Jones were huge again, it looks like something will happen every time Elliot Daly has the ball and Jack Wallace came on and did a great job.
"All our players are talking about the youngsters coming through so the future looks good."
Young is also pleased to have 20-year-old wing prospect Christian Wade, who marked his return from three months on the injured list with the try which sparked the Wasps revival, back for the run-in as his side, second from bottom of the Premiership, battle to stay above basement club Newcastle.
"He certainly gives us that bit of zip. He's a threat to any opposition defence," said the Wasps chief who was pleased his side emerged without any more serious injuries.
Winger Richard Haughton was replaced at half-time because of an Achilles injury, former Scotland full-back Hugo Southwell followed two minutes later with an arm injury and centre Ryan Davis, scorer of the second try, took a bang on the knee.
But Young expects all three to be fit for next Saturday's visit to Premiership leaders Harlequins, along with scrum-half Nic Berry, who missed the Biarritz match as he recovers from concussion.
"It doesn't look like anyone's put themselves out for next week, which is important for us," he said.
Desperate to avoid a last-day relegation crunch match when Newcastle visit Adams Park, Young added: "We are not out of jail in the Premiership - we need at least another win and we don't want to leave it to the last game.
"Our focus moves on to Harlequins now and we know how difficult that's going to be."
Victory secured Biarritz a home semi-final against the winners of Sunday's clash between their Brive and Welsh side Scarlets.
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