Premier League clubs, including West Ham, last month voted in favour of rules restraining wages and Allardyce is worried about the ramifications on his job.
He said: "If Financial Fair Play restricts the growth of West Ham then that's a concern for me, because you can't bring in the players you want to bring in.
"I'm looking to build a team for the Olympic Stadium, if those restrictions are stopping that progress then that's a difficult thing for me as a manager, because I carry the can.
"The player or his agent won't accept Financial Fair Play, certainly not in the early years. At the moment a top player will go and find somewhere else and somewhere else will pay it.
"It won't reduce the demands from players immediately and as managers we will all have to suffer that transition. We have a group of fans that want us to win and play well and if you haven't got the resources the results will suffer. We all know what happens then - and that's the sack."