The incident took place following Chelsea's stormy Barclays Premier League clash with Manchester United in October.
A Football Association independent regulatory commission on Thursday handed down Mikel's ban, which included a £60,000 fine, after the Chelsea midfielder admitted the charge.
In a statement the FA revealed the sanction would have been "significantly longer" but for the fact Mikel had believed he had been racially abused by Clattenburg.
A strongly-worded statement from Prospect on Thursday night, however, criticised the length of Mikel's ban, which rules him out of domestic duty until Boxing Day.
"Prospect, the referees trade union, today expressed dismay at the lenient punishment handed down by the FA Regulatory Commission to Chelsea player John Obi Mikel," the statement read.
"It is vital that officials were given real respect and this decision regrettably gave entirely the wrong message. A player in parks football found guilty of behaviour like Mikel's would have faced a long-term ban."
National secretary Alan Leighton claimed Mikel's behaviour deserved a heavier sanction despite the mitigating circumstances.
"For entering the referees dressing room and threatening and intimidating the referee to the extent that he feared for his safety the penalty was no longer than had the player been sent off for serious foul play," Leighton said.
"This did absolutely nothing to further the Respect campaign."
Leighton added that "far too much weight had been given to the mitigating factor and that Mikel's behaviour merited a strong deterrent penalty".
The FA announced Mikel's charge last month in a statement that also confirmed they would take no action against Clattenburg following a complaint by Chelsea that he used a racist remark to their players.
The FA decided there was "no case to answer" over the allegation the referee said "shut up you monkey" to Mikel.
Following Thursday's hearing, which Mikel had requested, the FA's regulatory committee revealed those factors had played a key part in the length of the ban.
"The breach of FA Rule E3 was in relation to an incident which occurred in the match official's changing room at the end of Chelsea's fixture against Manchester United on 28 October 2012," the FA statement read.
"The Regulatory Commission's independent chairman Christopher Quinlan QC emphasised that the Independent Regulatory Commission accepted, as did The FA, that at the time he threatened the referee the player genuinely believed that the referee had racially abused him.
"But for that factor the suspension would have been significantly longer."
Mikel, who signed a new five-year deal on Wednesday, will therefore miss the weekend's trip to Sunderland but will be available when Chelsea jet out for the Club World Cup in Japan next week.
His availability when the Blues return from the Far East could be limited though, with the midfielder due to meet up with Nigeria early in the new year for the African Nations Cup.
That tournament begins on January 19, with the players set to convene in the weeks beforehand, and Mikel would be unavailable until February 10 should Nigeria reach the final.
New boss Rafael Benitez appeared to begin preparations for his absence last night when he employed David Luiz in midfield at stages of the 6-1 Champions League win over FC Nordsjaelland.
Benitez admitted after the match he was prepared to use Luiz further up the pitch and provide support for holding midfielders Ramires and Oriol Romeu, who both started last night's game.