The Hammers had Carlton Cole sent off during Saturday's 2-1 home defeat against Everton for a high tackle on Leighton Baines, although referee Anthony Taylor's decision to dismiss the striker seemed to be a harsh one.
Everton's Darron Gibson also saw red in the closing stages of their win for a similar offence, but Allardyce beleives it is time for football's governing bodies to implement the use of technology to help officials make the correct decisions.
"The only way to make it better for us all is to bring technology into it," he said.
"I always said that two and three challenges a game should be in our favour. We should be allowed it, should allow technology into the game.
"Forget about your old (Michel) Platinis, who are antiquated.
"I know they're in strong positions and they affect the game but they're not doing us any favours by not allowing technology to come into play.
"The technology today means it's done in less than two minutes, isn't it - at the absolute most.
"I had two TVs in the dugout and it used to be a bigger help for me on the fact that I thought what decision the referee had or hadn't given.
"The fourth official could see that it wasn't an offside, or it was or it wasn't a goal - at least you knew it was or it wasn't."
Allardyce also revealed he had the televisions installed in his dugouts whilst manager of Bolton and the 58-year-old criticised the FA for removing them.
"We put TVs in the dugouts in 2005 and had them ripped out by the Premier League in 2006, that shows you just how backwards they are doesn't it?," he said.
"In fact we had two TVs in the dugout - one had a 10-second delay and the other showed replays of incidents."
Allardyce insisted the club would look to appeal against Cole's red card but, if the ban is upheld, West Ham will be without a main striker for the next three games with Andy Carroll also ruled out through injury.
The Hammers were due to travel across London to face Arsenal on Boxing Day but the match was postponed following the news London Underground staff will strike.
Allardyce said it was a blessing as he could not name a fully-fit side if he was forced to face the Gunners.
"I haven't got a team to play Arsenal," he said.
"I haven't got a team so it's worked out all right - we'll just come in on Monday and count up the bodies.
"We won't do any training and we'll just go and see how packed the medical room is."