A Football Association independent regulatory commission handed down the ban and a fine of £60,000 after the Chelsea midfielder admitted the charge.
The FA said in a statement that the punishment would have been "significantly stronger" but for the fact Mikel had believed he had been racially abused by Clattenburg.
However, Prospect criticised the length of Mikel's ban, which rules him out of domestic action 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".