With so little to choose between the two teams in wet conditions at the Twickenham Stoop, Armitage admits ill discipline cost the pre-match favourites dear thanks to Yachvili's outstanding efforts from the tee.
But rather than sulk about failing to finish off a job well done in all eight previous Amlin Challenge Cup ties, Armitage insists Toulon will be doing everything they can to ease the pain of defeat with a win over Racing Metro in this weekend's Top 14 play-off tie at the Stade Felix Mayol.
"We were beaten by an outstanding goal kicker," said Armitage, who was one of two Toulon players yellow carded in the second half.
"It was a chess game and Biarritz conceded fewer penalties than us, or at lest fewer in the most dangerous areas of the pitch.
"We gave Dimitri Yachvili the opportunity to shine. If we want to start winning titles we must stop giving away penalties in our half of the pitch.
"We wanted to bring something back from London for all of us, for the club and for our incredible crowd. Toulon haven't won anything for 20 years but we are very ambitious.
"I'm convinced we can bounce back - I'm sure about that. We have the qualities to finish the season well.
"Sometimes you must lose games to improve. It's a huge disappointment to lose the final but I am convinced we will perform better against Racing Metro and rewrite the history books for Toulon.
"Since Sunday we have been fully focused on Racing Metro. We have the opportunity to put the defeat behind us. The play off game in the Mayol is a huge game for us. It's a chance for us to bounce back and we'll be ready."