The club's director of rugby told Sky Sports News: "It was only Jonny's decision because he is the captain. Three of the kicks he missed were from long range.
"Jonny is not a robot, he is a human being like everyone else. We knew before the start that Exeter can play well but we also played well and the difference was good enough.
"It was important for us to win one game outside of France but the competition is not over yet. We have a number of injuries after this game with Bakkies Botha, Bryan Habana and Craig Burden but that is the way with rugby."
The result has left Toulon at the top of pool two.