But Dan Baker carved his way through Leinster's imposing defense before Ospreys piled forward in search of the winning score which ultimately eluded them, with Madigan nailing one extra kick from the tee than Sam Davies to make the difference.
And while Tandy tipped his cap to a professional job by the hosts, he was quick to point out that his youthful line-up had showed plenty of promise.
"It's a game we could have won but Leinster probably deserved the victory in the end," he said. "There's a hell of a lot of pride in the team once again though.
"We have some real talent coming through our ranks, everybody can see that, it's just about turning that promise into wins in the big games.
"We missed a couple of opportunities on half-time that could have set us up nicely, but we had people like Rhys Webb, Sam Davies and Dan Evans who were able to put us in good positions in the second half.
"Ultimately it was down to a couple of attempted offloads, a couple of errors, and the chances were gone. That comes down to experience and learning to manage the game.
"We bombed a couple of seven-pointers. At points of the game we built momentum, showed some real skill, but with a young group comes learning and maybe they need to understand when to offload and when to recycle.
"It was a pretty brave performance. It's a very young group with an average age of just 24 and being 16-3 down at the RDS, against a very experienced Leinster team, it would have been very easy for them to throw the towel in."
The losing bonus point did move the Ospreys up to seventh in the GUINNESS PRO12 standings for the time being at the expense of Glasgow Warriors, who play later on Sunday.
But after two tight encounters with the two sides at the GUINNESS PRO12 summit in successive weeks, Tandy believes it could have been so much better.
He said: "Looking back at the last two weekends we've come to Ireland for back-to-back games against the top two and it's been a mixed bag. We've played some decent rugby at times, but there's plenty of learning from the games as well.
"We could have taken five points against Connacht last week but ended up with nothing despite a huge effort. Ultimately though it's disappointing that we are coming away with only one point from the last two games, top two or not."
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