Antonio, 27, returned from a calf injury in February and has started just one of West Ham's last four league games.
"Joe Hart will start, " Moyes confirmed.
Those sitting directly in front of the directors' box chanted their disapproval towards co-chairmen David Sullivan and David Gold, who eventually departed the room.
West Ham have had more games with over 2.5 goals (59%), although it is notable that six of their eight home games under Moyes have had unders.
In a statement, the club said it had launched a "full and thorough investigation" and is "committed to taking decisive and appropriate action". "There will be no further comment at this time".More news: Nun in legal dispute with Katy Perry collapses and dies in court
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"Sometimes in life you come across challenges both on and off the field".
"The way you carry yourself in good times and bad times define you as a person", he said.
The Baggies are now eight points from safety with nine games to play, with Stoke, Crystal Palace, Southampton, Newcastle, Huddersfield, West Ham, Swansea, Bournemouth, Everton and Brighton separated by just seven points.
"All I ask for is that everybody sticks together and we try to get ourselves enough points to make sure we're a Premier League team (next season)".
West Ham are 14th on the EPL ladder, just three points above the relegation zone. "Footballers are all winners - we want to win every game so even with 40 points we are not going to put the handbrake on and stop showing up at the weekend".
He has told the board that he will want to make major changes to the squad if he stays, with as many as 10 players leaving.