Bastareaud was the top tackler for Toulon, who will now turn their attention to this Saturday's Top 14 semi-final with Toulouse.
And having ended a 21-year drought for a top level trophy, Bastareaud is keen to see Toulon carry their momentum into the clash with the defending French champions.
He said: "It's a little frustrating not being able to celebrate anything with our supporters.
"But we know that the semi-final comes quickly. We will enjoy this success, but on Monday, we will switch our focus to the Top 14. We have a chance to create history. Nobody thought at 15-6 to Clermont, we would be champions of Europe.
"We fought for 80 minutes, we gave everything. It's huge to win a title with this team, this group of friends. Before the game, nobody thought we could do it. It's beautiful.
"We knew it would be physically taxing but we held our nerve, showed we had the guts. I came here to experience moments like that."