A number of decisions, especially at the breakdown went against Quins and stopped them gaining momentum. Next week's return in Toulouse is now critical to their chances of making it out of Pool 6.
"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 and find ways of being more physical," said O'Shea.
"I'm proud they gave us the respect we deserved after 14 games unbeaten. But we've got to get used to playing at this level.
"In the end the right side won. We made a few mistakes, they were incredibly physical and we didn't win the gain-line battle.
"We clawed our way back into it but that second try was a sucker punch. They really attacked the breakdown with an unbelievable ferocity.
"The crowd was magnificent and they witnessed a great European side. Toulouse will be a tough challenge for everyone.
"The lads are battered and bruised and disappointed, but they are not down. They will be battered for a day or two, but then will be ready for the next job."