The Official Online RBS 6 Nations Store is open. The store has everything you need to get behind your team during the RBS 6 Nations, plus the store is now fully stocked with a much wider range of rugby merchandise.
Davies said: "We stuck in there and we deserved the win for sheer blood and guts if nothing else.
"We worked hard, kept our head down, been very objective in our approach and it paid off."
The Scarlets got their two tries through Gavin Thomas and Nathan Brew either side of half-time.
Thomas drove from a line-out to score and Brew picked up from Jonathan Thomas losing possession to race through and over the line.
But Ospreys assistant coach Sean Holley rued his side's own missed chances.
"It's bitterly disappointing from our perspective," he said. "We came here to win. We felt we had a good enough side and a good enough challenge to win the game.
"We were up against a very dogged and determined Scarlets defence and we just failed narrowly to break that down.
"I think we missed a few opportunities in the second half to nail the game home. We felt we were in control but could kill the game off."