Treviso duly obliged with a thumping 41-17 victory at Parc Y Scarlets but try as they might, Ospreys could not inflict defeat on Leinster, who ran out 37-19 winners in Dublin, thanks in the main to Andrew Conway's hat-trick.
The Ospreys did their best to battle back and did score three tries through Dan Biggar, Ben John and Tom Isaacs but when Cian Healy forced his way over on 78 minutes the game was up for the defending champions.
"I'm disappointed that we've not managed to make the play-offs, especially after Treviso did a job over the Scarlets," said Tandy.
"I spoke before the game about not wanting to throw the towel in then going into the changing room and discovering the Scarlets had lost.
"That wasn't the case, we gave absolutely everything and showed more of what we are about. I'm proud of the effort and the attitude that we've shown out there. That reflected who and what we are, but unfortunately it wasn't enough in the end.
"It's just one of those nights. It's been one of those seasons, definitely. The bounce of the ball at crucial times didn't go our way and we're left looking at a scoreboard that doesn't really reflect the way the game went, I don't think, but all credit to Leinster, they showed what a quality team they are."
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