Alan Leighton, national secretary of referees' union Prospect, has described Sir Alex Ferguson's apology to Alan Wiley as 'half-hearted'.
The Manchester United manager launched a scathing attack on Wiley after his side drew 2-2 with Sunderland at Old Trafford last week.
The Scot accused Wiley of being unfit and complained that the official slowed the game down when he was booking players because 'he needed a rest'.
Ferguson has recently apologised for the furore caused by his comments but has maintained that he stands by his belief that referees in general struggle to keep up with the pace of the game in this country.
"I think it's a half-hearted apology at best really, and it probably exacerbates the position, rather than resolving it," Leighton said.
"He clearly hasn't retracted the statement about Alan being unfit so it's not an apology for the main offence caused - and then he widens it to question the fitness of other referees, so he seems to be opening another can of worms which I don't think is very helpful at all.
"Referees are fit, they have sports scientists who test them regularly throughout the season. They don't just pass a fitness test at the start of the season.
"Their body fats and BMI are regularly monitored, there are get-togethers every two or three weeks where they are put through extensive training and testing."
Ferguson has been asked to explain his comments to the Football Association by Friday and could face a touchline ban or a hefty fine.
"I think the punishment should be a UEFA-type coaching ban, which is rather more than a touchline ban," Leighton continued.
"Referees always accept decisions are going to be pored over - they have no problem with legitimate criticism.
"What's problematic is when the integrity and key components of refereeing are being questioned in a totally unwarranted and unfounded way - and we will defend our members when they are."