Scarlets still had the chance to win it, but Steve Shingler saw a last-gasp penalty sail wide and the victory was Ospreys'.
Tandy, though, spent no time revelling in becoming only the second team to beat Scarlets on home soil in 23 attempts.
"It was a good win. I know how much the boys have put into it and it's been a huge effort from us," he said.
"There are a couple of things we would like to tidy up, but it was a test of character and I think we came through that.
"Our discipline wasn't good enough and it's something we have spoken about.
"We gave away something like 14 penalties and a lot of those were in the middle third. We gave the Scarlets too many entries and cheap points, where we went off our feet or hands on the floor.
"We also haven't defended like we'd want to defend, we didn't ask enough questions in terms of the Scarlets when they had the ball in our 22 but we'll pick these things up with the boys on Monday.
"But, they keep recovering, keep going at it, and as a coach I'm pretty proud of my players, how they keep going about their work, how they keep battling and keep getting through things.
"The Scarlets have got a tremendous home record and I know they were putting huge importance on the game and the fact how much of a gap they could open up on us, but we've come down here, have done a job of work, and it's great to take four points home."
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