After a poor first-half display, Mel's side found themselves two goals down at the break thanks to strikes from Palace new boys Tom Ince and Joe Ledley.
West Brom pulled one back immediately after the restart through a debutant of their own, Thievy Bifouma.
Referee Chris Foy pointed to the spot and Chamakh tucked the penalty away to put an end to any hopes West Brom had of claiming anything from the game, leaving Mel to cut a frustrated figure as his side dropped into the Premier League's bottom three.
"Of course the penalty decision was laughable," he said.
"If it was a penalty then it would have been a red card and I think that the penalty decision really did prevent us from getting anything from the game.
"In the previous piece of play Julian Speroni made a great save and that would have made it 2-2 so the penalty decision killed us off really.
"If it was a penalty then we wouldn't be able to say anything about it but it was an error from the referee."
"I'm extremely angry," he said.
"The first half we gifted it to Crystal Palace. Now we have 13 very important games to ensure West Brom are in the Premier League.
"The first thing is to try to win the game on Tuesday (against Chelsea) and if we want to remian in this league then we must play like we did in the second half against Liverpool and the second half today.
"We have 13 cup finals and 13 battles and we must win as many as we can and the players must come with me on this battle."
