The England Saxon, who had missed 14 points with the boot during the game, got the Premiership leaders back to winning ways with a late 30-metre kick from out wide.
And O'Shea said: "Rory Clegg showed incredible bottle and you have to separate things with a fly-half - his general play bar one or two touch kicks, the way that he marshalled the team and got a pattern going was magnificent.
"He is an 80%-plus goal kicker - he wasn't today, you have those days. His fault will be that he took on two early kicks into a diagonal breeze which he probably shouldn't have but he showed incredible bottle to land a really difficult kick."
Quins had a narrow 8-6 interval lead thanks to a try from scrum-half Danny Care, after he took a quick tap penalty, and a penalty on the stroke of half-time from Clegg, with the Chiefs replying through two penalties from fly-half Ignacio Mieres.
The scores remained unchanged until six minutes from time when replacement fly-half Gareth Steenson looked to have sealed the game for the Chiefs with a 40-metre penalty.
Clegg soaked up the pressure and coolly slotted his crucial kick between the uprights but Exeter kept battling away and Steenson could have snatched victory, only for his 30-metre drop-goal attempt to sail wide.
O'Shea said: "Four days after our last game, I thought we played with incredible ambition, some good line breaks and off-loading, and I thought that we should have won the game quite comfortably.
"But they stayed in the game and we knew they would looking at their record of coming back in the second half - look what they did against Sale and the Dragons - but I thought we played some magnificent rugby.
"But I credit the guys; to give away a penalty to put them into the lead with six minutes to go (and come back), these are the wins. This is a tough place to come; I was not expecting it to be easy and it wasn't."
Harlequins end 2011 at the top of the Aviva Premiership table having lost just once - to reigning champions Saracens, while Exeter's losing bonus point from a second successive Premiership defeat took them up to seventh in the table, above Gloucester who face Saracens on Sunday.
"I can't stand here and say that we should have won the game," said Exeter's head coach Rob Baxter.
"You can't expect an opposition goal-kicker in the Premiership to miss that many opportunities.
"But that said, we finished with our usual grit and determination and worked hard to conjure a match-winning moment a couple of minutes later in the game.
"I am a little disappointed, primarily with our discipline because we're not a side that just go in the side of breakdowns and cough up soft penalties. We pride ourselves on making teams work very hard for their points.
"I'm pleased with our endeavour; I'm pleased we were in it at the end and I'm pleased that there was an opportunity to win it at the end, but I am disappointed with elements of our game. "
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