The young prop, who has been tipped to break into interim coach Stuart Lancaster's RBS 6 Nations squad, was stretchered off in the second half with a hip injury.
That loss added insult to injury after Timoci Matanavou's double was enough for the four-time European champions.
O'Shea said: "We are a good enough side to compete with teams like this on our day but we need to be more accurate in what we do, find ways of being physical.
"The right side won. They were incredibly physical. We didn't win the gainline battle and made a few mistakes.
"We clawed our way back into it but that try (Matanavou's second late on) was a sucker punch."
Meanwhile Ireland's Stephen Ferris was amongst the tryscorers as Ulster secured a much-needed bonus point win against Aironi to keep their Heineken Cup ambitions alive.
Brian McLaughlin's men eventually ran out comfortable 31-10 victors as Adam D'Arcy, Andrew Trimble, Paul Marshall and Paddy Jackson all touched down while Tommaso D'Apice scored Aironi's consolation.
And Scotland's Dan Parks was the hero for the Cardiff Blues in Pool Two as he kicked his side to a 25-8 win against Edinburgh.
Parks notched 20 points with the boot, including four penalties and two drop-goals, while Alex Cuthbert scored the Welsh outfit's try as Edinburgh could only muster a Lee Jones try and a Greig Laidlaw penalty in response.