It was scrum-half Kieran Marmion, on his 56th successive Connacht appearance, that scored the only try of the game to hand the hosts victory at the Sportsground.
Connacht had lost their last 11 all-Ireland clashes, but overturned a 9-3 half-time deficit to leave reigning champions Leinster dumbstruck.
And, after seeing just three Ian Madigan penalties trouble the scoreboard, O'Connor admits Leinster need to be more ruthless in attack when Cardiff Blues visit the RDS Arena on Friday, with tickets available here.
"I thought we were very, very good in the first half, but we didn't take our chances," O'Connor told the club's website. "Connacht were good in the second half and scored from the one opportunity they had.
"We weren't clinical enough. We had two or three genuine try-scoring opportunities that we didn't take - that's 20 points, you take those and it's a different ball game. One was brought back by the TMO and the other two we weren't good enough.
"We lost by a point to a very, very good Connacht side. A full house out there, they were very motivated and they've been playing good rugby.
"We need to go back and look at ourselves and make sure that we're better than that next week."
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