Rovers had twice taken the lead, going ahead inside four minutes through Steven Nzonzi's header, before eventually being outclassed by the rampant Gunners, who are now the top scorers in the Premier League.
However, it was the decision not to point to the spot and send off defender Thomas Vermaelen for what replays suggested was a trip on David Dunn at the start of the second half, when Arsenal led 3-2, which irked the Blackburn manager.
"I don't want to detract from Arsenal but it was a blatant penalty," Allardyce said.
"There is no doubt in my mind that the position of the referee was excellent. He just didn't, unfortunately, give the decision in our favour.
"It is human beings in a very big pressure position.
"In the big pressure pot that is this league, you have got to get the major decisions right otherwise you don't stay in this league too long, not as a manager or a player, so as a referee you have got to be judged the same.
"They are fully professional now so if they are not good enough, we should find someone who is.
"That decision wasn't good enough for me today and it had a major effect on the course of this game."
Allardyce added: "I try not to say too much publicly and say it through the system, but unfortunately the system is not working.
"So I have to be heard and people may say it is bitter or twisted, but I know I am 100% right because I am very professional in what I do.
"I research everything and [referees boss] Keith Hackett knows I am right."
Allardyce felt if the decision had gone Blackburn's way, then the visitors could well have got something from the game.
"At that particular stage you would see us getting a penalty, probably scoring it, them going down to 10 men - because it is a red card for stopping a goal-scoring opportunity - and the balance swings in our favour," he said.
Walton had earlier played a good advantage which allowed Vermaelen to go on and smash in an equaliser after 16 minutes.
David Dunn's deflected effort put the visitors back in front, but Robin van Persie and Andrey Arshavin saw the Gunners lead at the break.
Captain Cesc Fabregas got the goal his performance deserved just before the hour, and then helped set up substitute Theo Walcott, with Nicklas Bendtner cracking in a sixth late on.
Arsenal manager Arsene Wenger hailed his team's majestic performance, played out in front of both Arsenal legend Thierry Henry and England manager Fabio Capello.
"When we are confident we have a flow that looks like the goals will come at any moment and from anywhere," said the Arsenal manager.
"They enjoy what they do. They enjoy to play together and that for me is most important.
"There is some strength coming out of this team, we have to add some discipline defensively.
"We looked always like we would score goals.
"It's difficult to have so many people going forward and as well have everybody straight away defending well.
"It's a consequence of our philosophy a little bit."
Fabregas kissed the badge on his shirt after scoring, a signal to those who doubt his commitment to the Arsenal cause.
Wenger said: "It's the best answer to play well on the football pitch and to show you are happy to be where you are."
Should Arsenal win their games in hand, they could be just a point behind leaders Manchester United.
Wenger added: "We are in a strong position, despite the fact we have lost two games.
"If you look at the away games we had, it was at places where other teams can drop points - Manchester, Everton and Fulham.
"We should have won the two games in Manchester but that made our resolve even stronger.
"But let's not just look at Manchester United. We have also Chelsea, Liverpool and maybe Manchester City. The most important thing is for us to play at that level and get stronger and stronger."