The events in last month's Manchester derby has focused the spotlight on player behaviour, and the passions at Ewood Park when Blackburn host Burnley are likely to be no less intense.
It is more than 45 years since these most bitter of rivals last met in the top flight and Allardyce will tell his players they need to exercise control both to win the match and avoid any disciplinary problems.
The Rovers boss also believes referee Chris Foy needs to play his part in maintaining calm.
Allardyce said: "It's a huge responsibility, not only for the players but the fans and the officials.
"I will be emphasising to my players not to over-react which can happen with the adrenaline rush which comes in this particular derby.
"Sometimes the red light comes on, the red mist comes down and I hope that's not going to be any of our players on Sunday.
"I'm not trying to put any extra more pressure on the officials - Chris Foy and his assistants are very experienced so they will understand what it's about.
"Chris will have handled derby matches before and will know what's going on and calming players down with the right word in their ear at the right time will be very important."
The clubs' last meeting came in 2005 in the FA Cup fifth round, when Rovers triumphed in a replay, but Burnley won the last top-flight encounter back on New Year's Day, 1966.
For the last two decades however the Clarets have been in the shadow of their rivals - Blackburn are currently on their longest-ever consecutive run in the top flight.
Allardyce added: "This match has been talked about since Burnley got promoted as it has been so long since they met each other in the league.
"We have been in the Premier League for 10 years now and are an established top-flight side so that means everyone expects us to win but it's not like that in a derby.
"Form goes out the window and it's about who copes with that extra pressure the best.
"We have to have controlled aggression in the right areas and not get involved in any of the atmosphere that may cause you to go over the top and get booked or sent off.
"I hope it's a competitive rivalry without something that's going to go to far. The place is going to be packed to the rafters and that's what you want when you wake up in the morning looking forward to the game."
Allardyce turns 55 on Monday, and knows all of Blackburn will be wanting to wake up with a smile on their face on his birthday.
"It would be a nice early birthday present for me if the lads can pull it off," he said.
"For the fans we feel we have to win. We know the responsibility that lies on us.
"I'm sure many Blackburn and Burnley fans work together and we want the Blackburn fans to go home as happy as they can be and looking forward to getting up and going to work on Monday morning and bumping into that Burnley fan saying 'we've got one over on you'."