However, the same cannot be said for the Welsh region, who must string together a fruitful run-in and hope Glasgow Warriors slip up.
The two sides have met plenty of times over the years and O'Connor knows the task at hand - but the reward of severely denting Ospreys' playoff hopes is a sufficient carrot.
"We've played (Ospreys) enough to know enough about them. It's a huge game for them because if they lose they're probably out of it mathematically," said O'Connor.
"From that perspective they'll be doing everything they can to get the result and keep them in it.
"We've got to bounce back and we've got to make sure we fix the things that went wrong on Sunday.
"They're very hard to beat - they're hard to break down at home. They race off the line. They've got a good set piece. They've got a lot of Lions and Welsh internationals.
"We're under no illusions of how good they are at home. We're just going to make sure that we're better."
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