Last weekend's 41-35 triumph was particularly sweet for the Irishman who was part of the Quins side beaten by a last-minute Newcastle Falcons try back in the 2001 Tetley's Bitter Final Cup Final.
"I was here six years ago with Harlequins in the Tetley's Bitter Cup when we got beat in the last second of the game, so personally it's great to get a winners medal rather than a runners up one," said Burke.
"It was such a tense game again. The Ospreys are a very dangerous side. With guys like James Hook, Shane Williams and Lee Byrne they're capable of scoring tries from anywhere, and they did.
"We had a dream first half. We started slowly - they kicked two penalties - but then we started to believe in ourselves, we had one or two lucky breaks, the bounce of the ball went our way and we took our chances well.
"We probably allowed them back into the game in the second half. We gave away a couple of turnovers to allow them possession and we know how dangerous they are. They had nothing to lose. They had to throw everything at us and, credit to them, they scored a couple of good tries to bring them back into the game.
"It was a very tense final fifteen minutes and, in the end, it was great to get in the right positions at the right time. I think our experience and the know-how of the guys up front pulled us through."
The Irish international, who was with Munster when they won last season's Heineken Cup, hopes that that sort of experience will hold Tigers in good stead for a demanding end-of-season run in.
"We take every game as it comes. It was very important for us to turn up and put in a performance and that's given us all a boost. It's given us confidence going into next week and the big games ahead. It's great to win some silverware and the support was fantastic. It was a great day for everyone involved and hopefully they'll be more to come."