Webb had earlier looked to inspire a comeback with Tandy's men 16-3 down shortly after the interval.
But despite his interception and try from CJ Stander's pass, followed by Jeff Hassler's sensational burst through the middle, earlier tries from Denis Hurley, Simon Zebo and Paddy Butler were ultimately enough for the Munstermen.
Ospreys were not to be the first side ever to win a GUINNESS PRO12 semi-final away from home, and Tandy admits going from celebrating to comforting his players in a matter of moments was a bitter pill to swallow.
"There was a bit of excitement from us initially, but the result is obviously bitterly disappointing when we thought we'd snuck a win away from home," he said.
"But ultimately Munster deserved the win and congratulations to them for getting into the final.
"I'm very proud of the players and I think the fact that we never give up is something that has stuck with us all season.
"We are a very young group and they showed a huge amount of character out there. I think a lot of teams would have folded at 16-3 down, but we found a way to pick up a couple of tries.
"We always felt that we were in the game and we had some amazing individual moments, even though perhaps we left a couple of tries out there.
"We had a huddle on the field after the game and obviously there are a few emotional boys and a lot of disappointment, but I think ultimately when we look back there are a lot of proud moments from the season.
"And with the youthful team we've got, to come away to Thomond Park and be a TMO decision away from being the first team to ever win a GUINNESS PRO12 semi-final ever is something I'm very proud of."
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