O'Shea saw his side pushed all the way by their visitors before clinching a win in the final stages of the match.
"Disappointing game - no momentum," was the damning verdict from director of rugby O'Shea.
He added: "It was the second week in a row that the opposition have given away 20 penalties against us.
"I hope their front five are alright because every single time there was momentum in the game there was a player getting injured. I hope they're OK.
"Bur we had plenty of our own things we didn't do well. It's a win - that's all you can say. We're pretty disappointed.
"There was just no flow, no momentum, no nothing in the game.
"We gave them an easy try off the kick-off, trying to play, then we conceded another soft try.
"It's a good lesson. We've won it and the guys dug themselves out but there's a lot of frustration in the way that game flowed. Twenty penalties is a heck of a lot.
"It wasn't a good game of rugby, not enjoyable but we'll take the four points."
Worcester stuck to their task despite having opening try-scorer David Lemi and No 8 Semisi Taulava sin-binned but there were no apologies from rugby director Richard Hill for the way they disrupted the Quins game.
He said: "You have to do that to Quins. They like a fast, frantic game but that's the way it is."
Hill was, however, concerned about the 20 penalties his side conceded, and the fact that his scrum came off second best.
"The referee was really hot on the breakdown and we weren't rolling away.
"We weren't really listening to him because we were perhaps too keen to try and turn the ball over. We have got to learn from that.
"Looking at the front fives, we thought we should have dominated the scrum with the age and experience we had but it didn't happen."
But Hill was happy with the spirit his side showed to come away with a losing bonus point against the leaders, who only snatched victory thanks to a late drop goal from fly-half Nick Evans, who contributed 17 points.
"I was very pleased with the performance and the effort that went in," he said.
"We have had that passion, intensity and desire at home and tonight it was about trying to replicate that away from home.
"The players gave everything and we had a real belief that we could win.
"To come here and outscore them by two tries to one was a psychological boost for us.
"We are back on track and looking forward to playing Perpignan in the Amlin (Cup) on Thursday."
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