The French big-spenders fell to a 29-17 defeat at the hands of the Ospreys in the final round of the Heineken Cup pool stages.
But Toulon still qualify for the quarter-finals and will take on Perpignan in an all-French encounter set to take place in Barcelona.
And Wilkinson, who has racked up more than 100 points for the Lions, is keen to see his side kick on in the showpiece European tournament a year after they reached the Amlin Challenge Cup final.
"It was a spirited effort against a great team but the pressure told," said Wilkinson.
"We sat back and gave them too much ball.
"We've qualified and it's a hell of an achievement but we want to continue. Yesterday was a great lesson. We're keeping track of our lessons and we will make sure they count.
"You go into any Heineken Cup group and you expect a hard challenge. But in our group we knew we were up against it with some of the pillars of European rugby in recent times."
Wilkinson was the sole survivor from the team that dismantled Munster, with Philippe Saint-Andre ringing the changes, and the England fly-half has paid tribute to the players that came in.
"I don't think there are many teams that could pick a very different looking side and still come to the Liberty Stadium and compete," added Wilkinson.
"There's no first and second sides, we respect each other and it's more a case of horses for courses. The good thing about this club is everyone gets a chance."