The English champions were in irresistible form in the Italian rugby outpost, outscoring the RaboDirect Pro12 whipping boys by eight tries to two during a heavily one-sided contest.
Having knocked on the door last season, Quins now have their pool destiny in their own hands this time around and would appear to be primed for a full assault on the big prize.
O'Shea, however, wrote off their stunning performance as little more than a job well done, and rejected the notion that it sends out a message to the rest of Europe.
"It's one of those ones where you're dammed if you do and dammed if you don't," said the former Ireland international.
"Of course there is ambition in the club, but people will write today's result off as irrelevant. And they are more than entitled to do just that.
"All we can do is to continue playing as a team, and make sure we are in control of our own destiny.
"When we lose games we don't get carried away, and it's the same when we win.
"It's about being in with a shout come April and May.
"You can come here and do an unprofessional job and cause yourself problems which eventually come home to roost.
"But I was pleased that we did a professional job in very difficult conditions. To score eight tries against a team that stubborn is no mean feat."
Of the 57 points scored, 14 came directly from scrum penalty tries, with Sam Smith (2), Matt Hopper, Rob Buchanan, Ben Botica and Nick Easter also crossing the whitewash.
Easter was particularly happy with his touchdown, considering it was a first of the season.
"It was about time for me," he joked afterwards.
"People had been getting on my case about it.
"But really, today was all about the team rather than individuals, and I was pretty pleased about how we went about our business.
"We are representing our country as champions and we're delighted to have three from three.
"That said, we are only halfway through and we know from last year how quickly things can change.
"So we'll enjoy the food and wine that Parma has to offer tonight, and make sure we're ready to go back out and do a similar job next week."
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