Prospect claims that the official went "through hell" and not apologising is just one thing the club have done wrong, adding measures need to be introduced to stop similar casesChelsea must issue an apology to Mark Clattenburg after he was cleared of racial abuse.
Clattenburg is set to return to match duty on Sunday, where he will be fourth official for Tottenham's clash with West Ham, after the 37-year-old was found to be innocent of using "inappropriate language" towards Blues' midfielder John Obi Mikel in the match with Manchester United on October 28.
As well as Prospect condemning Chelsea for making the false allegations in the first place, they are also outraged that the west London club based their case on one witness, Ramires, and pursued it despite not knowing all the details. The union also urged the Premier League outfit to say sorry to Clattenburg.
"Chelsea have done a number of things wrong with this case," Prospect national secretary Alan Leighton told reporters. "Firstly, they made the allegation and the nature of it public on the Sunday of the match.
"Secondly, on the Wednesday after their detailed investigation they decided to go ahead with a formal complaint based on one single witness statement, from one person who supposedly heard the offending phrase.
"The FA statement makes it clear Chelsea didn't even know when the alleged comment was supposed to have been made during the game. No organisation in the world would say that was ever going to get past the barrier of evidence needed to bring a charge.
"Thirdly, they have not apologised to Mark, who has gone through hell. This is about an individual who has been badly wronged and there is not even recognition about what they have done to this referee and that is staggering."
Prospect are not currently considering legal action towards the Blues as they would rather the club came out with a formal apology and pay Clattenburg some damages. However, they did not rule it out taking action if there is no apology.
"That is not our intention at this moment," Leighton continued. "Our intention is for something to happen that avoids any need for legal action.
"We have been calling for Chelsea to make an apology and pay compensation because it's the right thing to do."
The union's national secretary has also called for further action to stop a repeat of falsely or weakly backed cases against referees, adding that Chelsea acknowledging their wrongdoing should help.
"There needs to be some form of deterrent to stop clubs going ahead with stuff like this, which has no basis and impacts so badly on the referee.
"Our concern is it could happen from any club and is more likely to happen again if there is not some acceptance by Chelsea that this was wrong and shouldn't have happened."