Toulon saw both Carl Hayman and Steffon Armitage sinbinned during the second-half at The Twickenham Stoop and Mignoni believes the extra exertion in wet conditions made life difficult for the pre-game favourites.
"The game was a very difficult one, especially when you play with 13 men against 15. We spent a lot of energy and it was obvious during the last 10 minutes that the team was exhausted," said Mignoni.
"Biarritz didn't play that much better than us - it was more like a chess game with a lot of kicking involved.
"There were lots of long kicks and some up and unders and it was all about winning yardage. It was a chess game and they won it.
"We wanted to play a more attractive brand of rugby but it was very difficult to do that with a wet ball. The rain changed the tactical aspects of the game.
"We're very frustrated but Biarritz led the game very well tactically and it was logical that they were in front from the beginning to the end of the game."
Mignoni's men were clearly downbeat after the disappointment of missing out at the last hurdle for the second time in three years following their 2010 reverse against Cardiff Blues in Marseilles.
The pain of coming so close but falling just short will linger for some time but they do at least have the chance to right some wrongs when they take on Racing Metro in the Top 14 play-offs this weekend.
"The team is devastated but we must congratulate Biarritz for their victory. They've had a difficult season in the Top 14 but they showed great spirit - just like us - but with better discipline," added Mignoni.
"I'm very disappointed for the team because the players wanted to rewrite the history of the club. They also wanted to win it for the crowd who have been waiting for a title for 20 years.
"But we have a second chance this weekend and that's very important.
"When you loose a final it's always tough to take but you must stand up again and find your energy. We will analyse the game but we must move on quickly and focus on the next game against Racing."