That was the Welsh region's second bonus-point triumph in as many weeks as Rhys Webb notched a try double and Canadian duo Tyler Ardron and Jeff Hassler also crosded the whitewash.
Ospreys were also impressive defensively and although Tandy was eager not to let his troops get carried away, he couldn't hide his pride at the performance produced in the west of Ireland.
"It was a huge effort," said Tandy. "To get a bonus-point win, away from home against the champions, it's pretty special.
"We have to be pleased with how it went. The boys dug in tonight and it is a good start for us.
"We knew that coming here we would be in for a tough evening and you look at it, 60, 70 minutes in, it's pretty close, there's nothing in it.
"It is only two games in, we have to remember that. We've got to back it up now.
"We've got Treviso next week and they've been really difficult opponents for Ulster and Leinster these first two games so we know we will have to be spot on.
"It would be easy to get carried away with two bonus-point wins but the reality is, we've been far from perfect in both games.
"That's a good position to be in, when you've got everything you could have wanted from the games but still have plenty to work on."
Guinness PRO12 Final 2017 Ticket Information: Fans can save up to 20% on selected tickets, and prices start at just €30 adults and €5 child, and be booked via www.ticketmaster.ie. For further information visit http://www.pro12rugby.com/final
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