Allardyce's men are away at Chelsea on Boxing Day, sitting pretty in fourth place in the Premier League - but the former Bolton Wanderers and Blackburn boss said things could have been very different if not for a 0-0 draw in January.
At the time, West Ham were in the relegation zone - but they frustrated their London rivals, who had 39 shots and 72 per cent possession in the clash.
Allardyce said if Jose Mourinho's side had broken the deadlock, he might have been out of a job.
"I might not have been here after that if we'd have lost," Allardyce conceded.
"Chelsea can beat you five or six [nil] on their ground.
"I think on the back of recent results it made the life of the owners even more difficult to get behind me.
"That's not water under the bridge that's water under the sea. It's in the Atlantic Ocean now it's that far gone.
"We're a completely different unit now, we are a completely different team and squad and we are enjoying out football and Christmas a lot more than we enjoyed it last year, but we've got the two hardest games in the next 48 hours out of anybody else."
Allardyce said he did not think West Ham would be having a big say in the January transfer window, claiming they did not have the funds to buy players - and they could cover the loss of Cheikhou Kouyate and Diafra Sakho to international duty.
"I don't think we need to go into the transfer window in January," he said.
"One, I'm not sure the players available will be sufficiently good enough to fit in my team and if there is a player available who is good enough and of the quality, can we afford him?
"And the rest of the squad are more than capable of coping for that short period of time for the loss of Cheik and Daf."
Sakho and Kouyate will likely be representing Senegal at the African Cup of Nations, with manager Alain Giresse set to name his squad for the tournament on Friday.
