The Hammers were unable to build on Saturday's crucial 3-0 victory over Fulham when they returned to derby action against capital foes Crystal Palace.
A first-half header from Marouane Chamakh put them to the sword and has left them looking anxiously over their shoulder - with only three points separating them from the drop zone.
Allardyce believes his players badly underperformed during a trip to fellow strugglers and also feels that the match officials had a night to forget - with Stewart Downing having a second-half effort contentiously ruled out.
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."
Things could have been even worse for West Ham, with tempers boiling over the final whistle as players from both sides clashed on the field.
Ravel Morrison was cautioned for shoving Palace defender Joel Ward in the face, and must now sit out Saturday's trip to Liverpool after collecting five yellow cards for the season, but he could easily have seen red for raising his hands to an opponent.
McDonald added: "I've been told there was an incident but I wouldn't like to comment.
"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."