The fly-half kicked over all of his side's points in France as they saw off the Tigers 21-15 in the last eight of the competition.
"It's a great victory for the club," Wilkinson told Sky Sports News. "It was a big occasion and this is a first for us.
"The joy and desire to play with this team, the energy and togetherness we feel, is what has kept me going."
Toulon's reward for beating Leicester is a semi-final clash with Saracens at Twickenham Stadium on April 28.