The match ultimately hinged on Mason's decision to award a free kick for the Toffees just outside the area when Noble brought down Ross Barkley with the Hammers leading 2-1 in the 80th minute.
Not only did it mean a second yellow card for the midfielder, but it also gave Leighton Baines another opportunity to score from a free kick - once which he took to draw the Toffees level for the second time at Upton Park.
After going down to 10 men, Allardyce's men went on to lose due to a debut goal from Chelsea loanee Romelu Lukaku, but he believes that the referee should take a portion of the blame.
"He's played the ball actually," the 58-year-old told Sky Sports News. "I've just had five or six looks at it before I've come out and I think the lad has took the chance to go down on the tackle, but you see Mark Noble plays the ball first and then the lad goes down.
"I know it looks like a free-kick but, from where the referee is, he has got to be absolutely certain in that area and the fact that it's Mark Noble, because he's going to get sent off.
"I think he made a huge mistake there. Mind you, other people might see it different."
West Ham have not won since the opening day of the Premier League season against Cardiff City.