The Hammers were beaten for the third successive match thanks to Mile Jedinak's penalty with Allardyce admitting that his players had let down the supporters.
"Fans are entitled to air their frustrations. They paid their hard-earned money to come and watch a game of football," The Mirror quotes him as saying. "They want you to win and score goals and we didn't do that so in many ways we've let them and ourselves down.
"We knew Palace were going to frustrate us and knew we had to be good enough and patient enough to break them down but, sadly, we didn't. Too many simple passes went astray.
"We should have sat in at 0-0 and making sure we picked up a point. The real frustrating thing is we gifted the game to them with the penalty."
West Ham are 12th in the Premier League table, having collected 37 points from their 35 games this season.