The Hammers were trailing to Marouane Chamakh's first-half goal when Stewart Downing thumped in what appeared a perfectly good equaliser.
But the goal was chalked off for an apparent foul in the area, where James Tomkins and Joey O'Brien had challenged for the ball before it fell to Downing.
Allardyce's assistant manager Neil McDonald said: "Sam is still a bit livid after the performance, not just of our players, but the officials.
"We feel a bit hard done by with the goal that we scored that was given as a foul. That stopped us getting on the front foot and getting back into the game.
"We saw the replays and couldn't work out where the foul was. Decisions like that cost people points, we were on the front foot, we were attacking, we created a good chance and it's been chalked off.
"It's hard to take really. We felt it must have been for offside, but apparently not."
West Ham starlet Ravel Morrison's frustration boiled over after the final whistle and the midfielder was lucky to escape a red card for shoving Palace's Joel Ward in the face.
Mason showed Morrison a yellow card, which means he will be suspended for Saturday's trip to Liverpool, after which West Ham could be in the relegation zone.
"I've been told there was an incicent but I wouldn't like to comment," added McDonald.
"I'm more annoyed that that's his fifth booking so that's a suspension.
"I think it's out of frustration that we didn't get anything out of the game."
West Ham are now just three points ahead of Palace, who looked doomed not so long ago.
Fresh from a 3-0 thumping of Fulham on Saturday, they are still yet to string together back-to-back Premier League victories since they were promoted last year, a statistic that could yet cost them dearly this term.
West Ham's mood was in stark contrast to their hosts, who celebrated their third win of the season in new manager Tony Pulis' first home match in charge.
Chamakh had only previously found the net once this season - which was still one goal more than he managed in five months on loan with West Ham last term.
But in the 42nd minute Barry Bannan whipped in a cross and the much-maligned Moroccan glanced in what proved to be the winner to lift the hosts off the foot of the table.
"It's a great result," said Pulis. "You have to win games to give the supporters hope and they were great.
"The more hope you give them the more they will back you.
"The players have been fantastic, absolutely wonderful from the first minute we walked in.
"Chamakh never stopped running. He's got good quality and is a good player, he just needs some confidence and hopefully that will give him some confidence to grow into the player we need."