But the West Ham boss said: "It is not politically correct in this country that type of thing so you have to accept the punishment.
"I think there are tackles that the referees miss that they should be more aware of. There was a tackle in the Liverpool game where a Liverpool player should have been sent off - that was more dangerous than Suarez biting Ivanovic.
"The referee didn't see it and play went on and nothing has been talked about that because of the Suarez situation. Sturridge's over-the-top tackle was a legbreaker and he managed to get away with that."
Allardyce added: "He (Suarez)just has to take it on the chin when he has done something like that and move on. He just has to stop that little fuse that keeps blowing in his head at some stage where he loses his cool.
"It is probably why he is so talented and as good as he is but he has got to try and learn from that and cut it out."