The Moroccan striker made just three appearances during a five-month loan spell with the Hammers last term.
However, the former Arsenal striker returned to haunt Allardyce on Tuesday night, scoring the goal which took Palace off the foot of the table and kept West Ham in the relegation battle.
Chamakh believes his performance settled a score with his former boss after feeling hard done by during his time at Upton Park.
"When I was at West Ham there was a really good atmosphere and really good fans - I just had a problem with the manager," he told the Daily Mirror.
"He lied to me. I came and he said: 'You will play with Andy Carroll'. I played just three games and after that I did not play one more minute.
"So I think it was a good response from me on the pitch. I am really satisfied."
Victory against the Hammers was Tony Pulis' first as Palace manager having taken over at the weekend and Chamakh insists he is doing all he can to please the new boss.
"I didn't know [Tony] Pulis before he came here," he added.
"Of course I know him from Stoke but I didn't know his mentality, his job, so the feeling is good at the moment.
"Like for every manager, I give everything. I have changed my game for him.
"I am playing a little bit more like a midfielder than a striker but it is OK."
Tuesday's strike was only the second of the season for Chamakh, his first since August, but the forward insists his goal is a strong team performance before personal gain.
"Maybe you don't believe me but I swear I really don't care if I score or not," he said.
"The people outside look at goals and stats, but my pleasure on the pitch is to work for the team.
"And sometimes when I don't score, but I play a good game and we win, I am as happy as when I score two or three goals."
Palace now have 10 points from their opening 13 fixtures, just three adrift of West Ham in 15th, and Chamakh remains confident the Eagles will still be in the top flight next season.
"We will do everything to stay up, I think we can be better," Chamakh claimed.
"If you want to make some money, bet for Crystal Palace to stay in the Premier League."