Allardyce insisted his side were robbed of a point at Chelsea by a blatantly incorrect offside decision by assistant referee Mike Cairns.
Cairns failed to raise his flag as Salomon Kalou tucked home an 87th-minute winner from six yards.
Allardyce though maintained that the defeat was all down to the assistant referee.
He said: "It is one of those decisions I wouldn't mind getting myself into trouble with to be honest. But unfortunately that would cost me money and I don't want to part with my money when I don't deserve to be parted with it.
"You can't say what you really think. But it hurts deeply - not just for me but the players in particular. A result has been taken away from us by no fault of our own - by an assistant referee that has got a horrible decision wrong.
"We have to take that on the chin, it can't be changed. We have to accept that disappointment but look at the positive side of the performance and continue by trying to get three points against Manchester City.
"You have to complain more when a decision like this is made and it has cost us a crucial result. We have had a poor Christmas and that point would have made us feel that much better.
"The players played very well and we took the game to Chelsea, particularly in the second half. We created some good opportunities and took one. We could have taken more of them and got something out of the game, even with that decision from the linesman.
"It is the worst decision I've had go against me this year - no question about that. From our point of view it is difficult to take but he can't hide from it. It can only have been his fear maybe - blind fear in terms that he had to make crucial decision at a particular time on Chelsea's home ground. But we can do nothing about that now."
Allardyce remains convinced the only way to prevent such controversy in the future is the introduction of technology.
He added: "I've been an advocate of it for years. The game is so finally balanced now and we are living in a more volatile world in the Premier League than ever before.
"These decisions put more pressure on you as a manager when results are not going in your favour. I wouldn't know where offside is now. The offside rule has perhaps thrown far too much pressure on assistant referees and referees themselves.
"This one was blatant offside. There is no argument about interference or non-interference. It has come off a Chelsea player and the other Chelsea player is two yards offside at least. The assistant referee is in a good line and there is only a blue shirt between our goalkeeper and the goal but the flag didn't go up.
"But video evidence is something that should have been introduced years ago. It makes life easier for everyone involved and stops the controversy that surrounds major decisions like that coming out after a game when you have been hard done by. The technology should be used in a positive way."