The Tottenham chairman was upset after Mullery said he was "not impressed" by Gross's credentials as a leading Swiss coach.
Mullery added that if the former Zurich Grasshopper coach turned out to be a success, he would praise Sugar for appointing him, but he doubted whether Gross was up to the job.
"We could all do what he has done in Switzerland," Mullery said. "He has won the Swiss championship but that is like winning the championship in Scotland. It is probably impressive in Switzerland but not in England. I like their chocolate but..."
He added: "Foreign coaches have done well over here. Arsene Wenger's team is a delight and we knew all about Ruud Gullit before he arrived.
"But who is Mr Gross? I am not impressed. I don't know who advised Mr Sugar. If it works out and he is a good manager I will bow to Mr Sugar. But Gross has to prove himself."
Sugar was scathing in his rebuff to Mullery, the former England midfielder who is now a television pundit. "I am totally disgusted by Alan Mullery's irresponsible outburst in response to the appointment of our new coach," he said, "particularly as the man has not put one foot in this country yet.
"I do not know how anybody who claims to be Tottenham at heart can make such an irresponsible statement."
The statement went on to criticise Mullery's track record as a manager and in particular his recent failure at Barnet.
"I was brought up on the basis that people in glass houses should not throw stones and while Mullery may have been a good player, his managerial career is not one to rave about and he is certainly no authority on management. He should have sorted his 'Barnet' out, and I don't mean his haircut."
Mullery responded: "There are not too many top managers come out of Switzerland. Probably the top one was Roy Hodgson [of Blackburn] - and he's an Englishman!"Reuse content