The French giants over-powered Harlequins 21-10 at The Stoop in the Heineken Cup, prevailing with two tries from the Fijian wing Timoci Matanavou and 11 points from Luke McAlister.
Harlequins briefly threatened a comeback at the start of the second half, with a try from Mike Brown, but ultimately they had no answer to the power and panache of Toulouse.
"The right side won," said O'Shea, the Harlequins director of rugby.
"They were incredibly physical. We didn't win the gain-line 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. They really attacked the breakdown with an unbelievable ferocity.
"We seemed to be the ones getting penalised at the breakdown. Not many bounces of the ball went our way but I don't want to talk about decisions.
"The right side won."
Harlequins are flying high in the Aviva Premiership after their record-breaking start to the season, but a Toulouse side in this mood are a different animal all together.
O'Shea admitted his men need to adapt quickly, with the return fixture against Toulouse in nine days time.
"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," said O'Shea.
"They gave us the respect we deserved after 14 games unbeaten, which I am proud of. We have to get used to playing at this level.
"The crowd was magnificent to fill The Stoop like that 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."
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