The visitors also saw Darron Gibson get his marching orders late on in Saturday's Premier League clash at Upton Park, with both decisions looking soft.
Cole, who scored the opening goal, was sent off for a foul on Leighton Baines, with Allardyce moaning: "It is how quickly the referee got the red card out. He couldn't wait, he didn't deliberate over the decision or anything.
"There is nothing much we can do about the result but we can appeal the decision and hopefully we can get Carlton down to a yellow card and get him off."
Allardyce revealed he had a chat with Taylor afterwards, saying: "I spoke to the ref but that is between me and him.
"We will go through the channels of 'reporting' that the system has in place and I will take that up and pursue it quite vigorously.
"If he is not getting the right feedback or coaching and is told it was OK and 'carry on', then we have got a big problem.
"When you are looking for consistency from referees, you look for consistency in the same game he is reffing and we didn't get that today and that had a massive effect on the result.
"We have to, unfortunately, take that on the chin and the punishment is twofold for us."