Quins were up against it when a vibrant Warriors side opened up an early 8-0 lead through Miles Benjamin's score and a Joe Gray penalty.
But a dominant display up front, culminating in a penalty try, and 11 points from the boot of Nick Evans secured a 16-14 win, Quins' 13th of the league season.
"We gave Worcester an eight-point start in a game we knew was going to be attritional - we weren't as precise as we should have been at times," said O'Shea.
"You would be pretty arrogant to think that you are owed anything before a game - you have to earn everything in this league.
"We know that - we weren't good, but we won. The massive plus was that, yet again, our pack - both at scrum and maul - were outstanding.
"Worcester are one of the best defensive sides in the league, but they played a lot of rugby in the first half and caused us trouble.
"We are more than happy to have won both games against Worcester this season, but we weren't happy with our performance.
"The effort of the guys was outstanding - the precision wasn't - but we won. We know we can play a heck of a lot better than that."
Worcester's battling display - to which Premiership debutant Gray contributed nine points - earned them a crucial bonus point as they look to beat the drop.
And head coach Richard Hill insisted - despite relegation rivals Newcastle's 19-10 win against London Irish earlier in the day - his side only have eyes for the upper echelons of the Premiership table.
"I'm not interested in Newcastle," he said. "You can see from the way we are playing at the moment that we are interested in moving up the table.
"The teams below us don't concern us in the slightest.
"If you look at the way we have performed and the points we have picked up in our last four games, that's not a team that is going to be worried about relegation - provided we concentrate fully every single game and prepare for every match as though it's an international.
"I have no issues whatsoever with the effort these boys put in and we're looking forward to hosting Saracens on Friday already.
"I thought we did a little bit more than just scrap for a point - I think we surprised Harlequins a little bit with our counter-attacking and we made some superb breaks in the first 20 minutes."
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