The players voted by a 14-9 majority to proceed with the game after a series of meetings on Saturday.
Republic of Ireland boss Heimir Hallgrimsson says the last few days have been the "toughest" of his career.
Ireland’s players wore black armbands during last night's 3-nil win against Israel, didn’t shake hands and bowed their heads during Israel’s national anthem.
There had been calls to boycott the game to protest the ongoing war in Gaza, and goalkeeper Gavin Bazunu opted out of the squad for the fixture.
The players voted by a 14-9 majority to proceed with the game after a series of meetings on Saturday.
Hallgrimsson has faced continuous questioning on whether next Sunday's second match with Israel will go ahead.
While the FAI's President Paul Cooke has defended their handling of the situation, saying he feels they dealt with it "quite well".
He added the there was "unprecedented coverage" of protests from the media, which Cooke feels lacked balance.
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