Anthony Taylor dismissed West Ham striker Carlton Cole and Everton's Darron Gibson during the Toffees' 2-1 win at Upton Park on Saturday but both red cards have since been rescinded following successful appeals. Allardyce reckons the pool of professional referees is not big enough to cope with the congested fixture schedule over Christmas and New Year and believes tiredness can lead to officials making the wrong call.
"This is a difficult period for referees," he said.
"Why do they always seem to make more wrong decisions now? It's probably because they are overworked and they are fatigued.
"The system has to be looked at and in my opinion it's because they are fatigued. Referees are travelling all over the country and out in Europe and have been since the start of the season.
"There's not enough of them. They try their very best to get things consistently right. But it happens every year around this time of year, the controversy.
"We had a couple in our last game and there have been many throughout football over the Christmas period.
"Fatigue is everything in terms of decision making. Once it kicks in you lose the ability to make those decisions correctly."
Former Blackburn boss Allardyce thinks more money should be made available for the training of new officials.
"We've had professional refs for 12 years and the Premier League and PGMOL (Professional Game Match Officials Limited) and Football Association should treble the budget and create an academy of referees," he said.
"They need to ease the load on the referees we have. The game needs to move on and look at recruiting better refs from all avenues."