Tries from Johnny McNicholl and Rhys Patchell gave the Scarlets the win over their rivals from West Wales at Parc y Scarlets.
Wales ace Leigh Halfpenny kicked two conversions and a pair of penalties to confirm the success and leave the Scarlets in a good place ahead of Racing arriving in Llanelli this weekend.
“We now turn our focus to Europe and get excited by it,” Pivac said.
“This time last year we didn’t start too well and we know if we want to do well in this season’s Champions Cup, then we can’t repeat that.
“I think the win over the Ospreys couldn’t have been a better game for us leading in to what’s going to be an even bigger challenge against Racing.”
Scarlets were outscored three tries to two by the Ospreys, but still came out on top.
Analysing his team’s performance, Pivac added: “We were really happy with the start we made. We defended everything the Ospreys threw at us in the first 20 minutes.
“We saw some very good defence in our 22. We had a lot of energy and when we got our main opportunity, we converted that.
“We were disappointed with the second twenty of the first half and we spoke about that at half time. There was no excuse for the gaping holes in defence and we let in a couple of tries that should have been avoided.
“From our point of view it was making sure we started the second half very well, like we did the first, and making sure we didn’t have that lull. We bought the energy and passion the game deserved.
“We’re happy to get that result and after last week it was a massive step up. The Ospreys are a totally different side. Allen Clarke has done a good job and they’re heading in the right direction.
“Hopefully we are as well and it was a much-improved performance against a much stiffer test than we’ve had. I think that puts us in a great position for Racing.”
