Toby Flood slotted five penalties for the visitors but he was outgunned by Jonny Wilkinson who contributed a 21-point haul.
Cockerill insists the Tigers have plenty to be proud of and he had no grievances with the devastating defeat.
He said: "We have no complaints over the result and no complaints with the performance. It was outstanding from both sides.
"It was a good contest and we pushed them all the way. We could easily have won, the effort was phenomenal, we never gave up and we were right in it until the end.
"But Toulon are a very good team and they managed to sneak it."
Cockerill confirmed Marcus Ayerza suffered a suspected fractured collarbone in a thunderous collision with Bakkies Botha.
But Cockerill allayed any fears over Tom Croft, who hobbled off on 38 minutes with a back spasm.
He added: "Tom got twisted at the breakdown and his back went into spasm. He will be fine."