Dan Biggar admits next week's game at English champions Northampton Saints will be a true test of Ospreys' European ambitions.
Ospreys romped to a comfortable 42-7 win over Treviso in their opening European Rugby Champions Cup game.
Saints lost 20-11 against Racing Metro in their opener but Biggar said unbeaten Pro12 leaders Ospreys faced a tough test next Saturday.
"We know they're going to come out full guns blazing," Biggar said.
"They will be hugely disappointed not to come away from Paris with probably a win let alone a bonus point.
"We know what's coming and they're going to be hugely physical and start as a train.
"It will be a true test of us but we've got every reason to go up there and believe we can get a result.
"Confidence is high but we're under no illusions - it's going to be a step up next week."
Ospreys will go into next Saturday's game at Franklin's Gardens on top of Pool Five after they outclassed Treviso at the Liberty Stadium.
Wales fly-half Biggar kicked 17 points in the five-try bonus point victory - a seventh straight win for Steve Tandy's team.
But Ospreys may be without number eight Dan Baker after he was carried off against Treviso with a neck injury.
"We have to be satisfied with five points at home in what could have been a tricky encounter," Biggar said.
"They've improved since we played them first game, so all in all it was a pretty good team contribution.
"We all contributed in patches and it's pleasing to get off to a good start with what's ahead next week.
"We're under no illusion that we're going to play lot better teams and come up against tougher opposition.
"But we can only play what's in front of us and what was in front of us was Treviso and we got the job done.
"Winning at home is so important in this competition but to pick up five points was crucial."