Following a totally one-sided first half Harlequins led 21-6. It should have been far more and a huge defeat for the Welsh seemed likely.
However, in a complete turnaround, Welsh played with great spirit in the second half to reduce the arrears to 24-19 and a remarkable comeback was on the cards before the visitors steadied the ship to run out 31-26 winners.
O'Shea was nevertheless left unhappy with the match official, who he accused of a catalogue of errors.
"I'm unbelievably frustrated, you'd have to go a long way to see worse," he said of Mr Roberts' display.
"Everything was wrong - it was incredible. The offside line was irrelevant, trailing runners coming back was irrelevant, backing into the maul, not releasing in the tackle - all irrelevant.
"We were 21-6 at half-time but bafflingly the penalty count was against us, how that can be?
"We have a feedback process for the referees but it's not actioned upon and it's very difficult at times."
Quins played some delightful rugby in the first half as Welsh seemed on course for a crushing defeat, and O'Shea was very happy with his players' performance.
"We played some magnificent running in the first 45 minutes and that's what we should be talking about - our full-back, Ollie Lindsay-Hague, dazzling people with his footwork." said O'Shea.
The second half saw Welsh raise their game, clawing back to 24-19 before Quins pulled away again.
Welsh head coach Lyn Jones was appreciative of his team's efforts.
"At half-time we were staring down the barrel," he said,
"We started the second half well, we were still in there and we needed to get the first score, which we did. We had a chance to win but their class and ability shone through in the end. They are a very good side and it's a pity more sides don't play like them.
"We are showing determination and spirit and are good enough to stay in this league."
Calf injury victim Gavin Henson was still absent from the Welsh line-up, but the head coach is optimistic he will be able to call on his services soon.
"I saw him last Saturday and he was due to train on Wednesday but his leg wasn't good enough," said Jones.
"Hopefully he will play as soon as possible but it's a calf injury and I don't want players to rush back."
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