Palmer and co led by eight points at the break and were back in front 26-23 on the hour after Wilkinson's boot had brought Toulon into contention.
And while the initial misery of seeing the potential for a first European trophy pass them by at the penultimate stage, the manner in which a young, under-strength Stade side troubled their star-studded opponents at least provided some crumbs of comfort for the England second row.
"It was very disappointing to lose a game like that by three points with a drop goal in the final minute. The feeling in the dressing was one of disappointment, but there was quite a bit of pride in the way we played," said Palmer.
"We went out there with a lot of guys who haven't played that much rugby recently. I don't think anybody really believed in us before the game but we went out and showed what we can do. We put in a pretty decent performance, especially in the first half.
"It wasn't a great start from us conceding a try in the first two minutes but we showed a lot of belief in ourselves and it was probably one of our best away performances of the season. We went to what is a really difficult place to play, we stuck together, believed in ourselves and showed some good spirit.
"I think we caught them on the hop a little bit in the first half but, fair play to Toulon, they're a quality side and they came back at us in the second half. Our discipline let us down at the start of the second half and the end of the first half when we gave away too many penalties.
"Jonny's so dangerous and, with such a strong wind, you knew giving away any penalties even inside your own half was a chance of giving away three points. We'd taken advantage of that in the first half."
Palmer, who won the Heineken Cup with London Wasps in 2007, was particularly impressed with a trio of youngsters whose individual showings suggested the future could be bright for the Parisians.
Stade are still battling to break into next season's Heineken Cup via the Top 14 and Palmer believes their rise to prominence bodes well for a sustained assault on the continent's top prize in the coming years.
"We had three young guys playing - Jules Plisson, Alex Flanquart and Hugo Bonneval - who were brilliant for us," added Palmer.
"Jules had a great game. He was kicking everything and he ran the game very well.
"I thought Hugo had a fantastic game at full back. He was really assured and looked very dangerous on the counter attack. That was the best I've seen him play. Hopefully, he'll take his chance, get some more game time and go on to better things."