Allardyce and Wenger have long been at loggerheads, with the Arsenal manager criticising the style of play employed by his Bolton and Blackburn sides on several occasions in recent years.
Ahead of the Arsenal's 2-1 win at Ewood Park last month, Wenger accused Stoke defenders Ryan Shawcross and Robert Huth of fouling Tottenham goalkeeper Heurelho Gomes in an earlier game, and he stressed that referees must ensure that rules are respected.
Wenger again spoke out about foul play when Abou Diaby suffered an ankle injury in Saturday's victory against Bolton, calling Paul Robinson's challenge an "unfair tackle", but he added: "Why should I create another story? You asked me how the tackle was and it was bad, but I don't know if my views are taken seriously. People just think I'm protecting my players by saying that and that I have a [vested] interest."
However, Allardyce said: "Arsene has most of the media in his pocket now and is almost - almost - affecting the officials so that you can't tackle an Arsenal player. That's something he's very clever at working on and it's almost working in his favour, you can see that.
"Read his interview before the Stoke City v Aston Villa match, what he said and how he said it - he's a very, very clever man in terms of influencing referees, officials and everybody in football.
"He can't be brought up for it because it's about another match - rather just before he plays us. There is a perception that we kick everybody and Arsenal's motivation is that you can't tackle us as you aren't supposed to.
"In terms of saying people are trying to injure players, he's trying to influence, through the media, the referees and that's something they shouldn't get sucked in to."
He added: "He's deflecting attention from the situation which says the game of football is a contact sport. You have to try to win the ball at all costs and if someone doesn't get it quite right people get injured.
"It was much more apparent in my day when people use to go out to try to hurt an opponent every week, but today it very rarely happens.
"I completely deny that my team deliberately injures players, certainly not. In the Premier League the commitment and speed unfortunately brings players together at such pace that it's almost impossible to avoid injuries."