Steve Staunton's Republic of Ireland are effectively out of the competition.
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Jankulovski's goal gives the Czech Republic an almost unassailable Group D advantage.
Reeling from the sending-off of substitute Stephen Hunt on the hour for a lunge on Jan Polak, Staunton's men battled bravely in search of an equaliser but were ultimately fortunate to go down by such a narrow deficit.
Staunton: "I thought it was very harsh. Stephen has won the ball and his momentum took him through. The player acted injured but was up running around when Hunty had got off the pitch.
"There was a lot of play-acting and I wasn't happy with their centre-half Radoslav Kovac. The referee looked like he was only going to give him a yellow card until Kovac said something to him.
"There were a lot of decisions but what can we do about it, it's history. But I'm sure the referee's assessor will have his own report. We'll just have to wait and see what is the outcome."