The Clara man can no longer qualify through the points system.
Shane Lowry's Ryder Cup hopes were dealt a massive blow after missing the cut at the Czech Masters at the weekend.
The Offaly man finished on 2-under following back-to-back rounds of 71 on Thursday and Friday, with the cut being capped at 3-under.
The result now means the 2019 Open Champion will have to rely on a wild card chosen by captain Luke Donald in order to represent Europe next month.
Meanwhile, Rory McIlroy ended his week in fourth on 14-under-par at the Tour Championship.
Norway's Victor Hovland was the overall winner of the Fed Ex Cup as he shot a final round 63 to claim the 18-million dollar first prize.
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