The Irish FA has revealed that Jonny Evans was the player fined along with Keith Gillespie for misbehaviour after the Euro 2008 qualifier in Iceland.
Gillespie was fined a larger sum for fighting on an aeroplane as the team boarded their flight to London.
Evans was not punished in relation to that incident but for drinking after the defeat in Reykjavik.
IFA chief executive Howard Wells said Evans' offence had been minor in comparison to that of Gillespie.
The money from the fines is to go to charity.
At first the IFA, although confirming Gillespie's fine, refused to reveal the identity of the other punished player.
Wells said they had then named both because some people were jumping to the wrong conclusion.
He also said the governing body, as well as the players, could learn from the affair.
"Maybe the IFA should have chartered a flight home straight after the game," said Wells.
"The players had free time on their hands and they were frustrated with the way the game was lost at the end of a long time away.
"We are mindful that it is a young squad and we hope that we can draw a line under this isolated incident for the good of the players.
"I feel sorry for the manager especially, because he came in at a difficult time, with four away games out of six to come.
"The press might be interested to know how many big-name managers did not want to go near it."
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