"But I do not know any more what is a foul and what is not a foul. Every time [a ball went in] Fabianski was pushed.
"There is no purpose to play the ball from the Blackburn players - they don't even watch the ball. He [Fabianski] had two players in front of him all the time and every time it was to stop him getting the ball.
"In football, when you don't go for the ball and you stop the keeper going for the ball, it is a foul. I think the referee cannot allow that. I am very disappointed the referee lets that happen in a football game, it is unfair to a goalkeeper."
Rovers boss Allardyce admitted his team had targeted Fabianski but argued that they did so within the rules.
"We know that the weakness for Arsenal is balls in the box and we did that positively," said Allardyce.
"We have seen that under pressure Fabianski's handling is sometimes suspect.
"We felt that the more balls we put in, the deeper Arsenal would go and the more bodies Fabianski would then have to go through."
Allardyce targeted 'weak Arsenal defence'
Van Persie headed Arsenal in front before David Dunn equalised shortly before half-time.
Chris Samba scored the winner after the break to ensure that Rovers will end the season unbeaten at home against the Gunners, Chelsea, Manchester United and Liverpool.
"It looked like the match would be a tall order after the first 15 minutes but we slowly worked our way into the game," added Allardyce.
Wenger's team have won just one of their last eight matches in all competitions and are not yet assured of third place in the table and automatic qualification to the group stage of next season's Champions League.
Manchester City and Tottenham, who meet on Wednesday, can still potentially catch the Gunners but they need Arsenal to drop points in their final game against Fulham next Sunday.
"I believe that it is about what we do, not what Manchester City and Tottenham do," added Wenger.
"We have a home game to finish the season and we want to finish well."
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