Wilkinson struck with just 45 seconds remaining at the Stade Felix Mayol to see Toulon overturn an eight-point half-time deficit and Mignoni was delighted with the spirit and commitment shown by his players, even if the overall performance was a little way from his liking.
"I'm not very happy about the rugby we played but to win a knockout game in that manner showed our strength of character," said Mignoni.
"It's good to get used to suffering in the way we did during a game of this kind and still secure a win. There's a huge difference between winning by one point and losing by one point.
"We weren't really in the game in the first half and we were lucky to come back into the changing room at half time with the score at 19-11.
"We didn't keep the ball well enough and we didn't win the territorial battle. But in the second half it was a much better performance and we showed good discipline.
"It was a complicated and tough finish but a great finish for us. The players are very happy to be through to the final but they're also very tired as it was an exhausting game."
The hosts had enjoyed a dream start with a Steffon Armitage try inside two minutes but Stade hit back in style with a Hugo Bonneval try and a fine first-half kicking display from Jules Plisson.
Wilkinson kicked his team back in front with 12 points in the opening 15 minutes of the second period but Stade still hadn't read the script and responded in kind with a wonderfully-worked try from Morgan Turinui.
That Stade score pushed the visitors 23-19 ahead on the hour mark yet it was Toulon who just about edged the mental battle in the final quarter.
With the scores tied at 29 apiece and the clock ticking towards the red, Wilkinson stepped up ala the 2003 World Cup Final to give Toulon a victory forwards coach Olivier Azam felt they deserved.
"In the first half, we certainly didn't plan to make that many mistakes," said forwards coach Azam.
"But thanks to a Jonny penalty just before half time, we came back into the game. We didn't panic and we were always confident.
"In the second half the wind was with us so it was easier to play in their half and dominate territory. We also put more pressure on them in order to get as many penalties as we could.
"I understand that Stade Français are disappointed - they played very well. I want to congratulate them because the fact that the game wasn't easy was down to their performance.
"It's important now to go on and win the title - it's something that will become part of the history of this club."