The home side were looking to end their campaign on a positive note, and a looping high ball from captain Stefan Johansen in the 71st minute forced Brunt's error as he tried to clear the ball from under the crossbar.
The Northern Irish, currently ranked fifth of the eight playoff teams with the top four being seeded, played plenty of tidy football but despite some late chances the game slipped away.
The Irish finished second in Group C with 19 points from 10 games behind world champions Germany who had a perfect record with 30 points. Czech Republic were third on 15.
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Europe's nine group winners qualify automatically for next year's 32-team tournament in Russia while the eight best runners-up enter a two-leg playoff for the remaining four berths.
(Reporting by Philip O'Connor; Editing by Christian Radnedge)
