Coetzee has overseen the worst season for South Africa since the country was readmitted to international rugby in 1992, culminating in a 27-13 loss to Wales in Cardiff on Saturday.
That was the eighth defeat in 12 Tests this year, including a first to Italy, a first at home to Ireland and a first away to Argentina.
The twice world champions were also humiliated 57-15 by top-ranked New Zealand - the largest home defeat suffered by the green and gold.
"I feel dreadfully sorry for Allister because he is a decent guy, but better Springboks coaches than him have been fired," said Mallett, an influential and respected TV analyst.
Jake White was told to reapply for his job after coaching South Africa to the 2007 Rugby World Cup title. He refused and was replaced by Peter de Villiers.
Former Springbok loose forward Mallett, 60, coached the Springboks for four years from 1997 before being ditched for saying Test tickets were too expensive.
"Test rugby is not a popularity contest - coaches have to win matches, and they do make a difference to teams," he said.
"Allister keeps telling us how well training went and how excited he is before a Test, but the Springboks keep losing.
"If a player messes up a drill, you tell him to 'get it right'. You do not say 'don't worry, it does not matter'."
"Look at England under Stuart Lancaster and Eddie Jones.
"Stuart was a decent coach, but his team were eliminated after the first round of the 2015 Rugby World Cup in England.
"Eddie comes in, chooses a new captain, makes a few changes in personnel and tactics, and now they are on a long unbeaten run."
Mallett said "it had been a dreadful season for the Springboks with no improvement from one Test to the next."
However, he doubted that Coetzee would throw in the towel after one season of a four-year contract despite growing media and public calls for his dismissal.
"Why would he walk away?. He has a four-year contract. What we do not know is whether there is a performance clause in it."
Recently elected South African Rugby boss Mark Alexander reacted to the feeble surrender in Cardiff by ruling out "knee-jerk" decisions.
"We are all feeling very raw and let down and it would be easy to make knee-jerk decisions, but we must resist that.
"It has been a profoundly disappointing season in terms of results and we are acutely aware that we have failed to live up to the Springboks' proud heritage.
"Our playing fortunes have been declining since the 2014 tour to Europe - despite a fine fightback to finish third at the Rugby World Cup last year.
"We must calmly and coldly analyse what have been the main factors contributing to those results before determining what remedies are at our disposal.
"I can assure our supporters and stakeholders that if tough decisions have to be made, we will not shy away from making them."
Alexander said the Springboks review process would start in December by talking to Coetzee and other team role players.
Coetzee, 53, succeeded Heyneke Meyer last April after a short spell coaching a Japanese club. Previously, he made the Stormers the most successful Super Rugby franchise in South Africa over six years.
His 2016 record is the worst for a full season since South Africa's return from apartheid-induced isolation in 1992.
Original source: Better Bok coaches than Coetzee have been axed - Mallett