Boycott said he would need to "black me face" to get a knighthood.
Gibson is reportedly set to join the Proteas after England's current series with the Windies, the former paceman now working as fast-bowling coach under Trevor Bayliss.
Knighthoods, he said, were handed out like "confetti" to West Indies greats - he named no names, but a total of 11 former Caribbean greats have been conferred the honour to date, including Sir Vivian Richards, Sir Garfield Sobers and Sir Curtly Ambrose.
The defeat by an innings and 209 runs in the first day-night Test in England at Edgbaston at the weekend left both Caribbean legends and old worldwide foes alike bemoaning what they saw as Windies cricket crashing to rock bottom.
"Mine's been turned down twice".
"Speaking at an informal gathering I was asked a question and I realise my answer was unacceptable", he wrote.
"I have loved West Indian cricket my whole life and have the utmost respect for its players", he added.
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A BBC spokesperson said: "He has rightly apologised unreservedly for these clearly unacceptable comments".
"I never saw any aggression from the West Indies players throughout the three days", added Ambrose, who took 405 wickets at an outstanding low average of 20.99 in his 98-Test career.
Controversial England batting legend Geoff Boycott made a grovelling apology on Tuesday for remarking he needed to "black up his face" to get a knighthood at an event last week.
Boycott was also inducted into the International Cricket Council's Hall of Fame in 2009.
According to another former captain Geoff Boycott in the Daily Telegraph newspaper, there could be no room for English gloating because the Windies surrender at Edgbaston had been so "painful to watch".
"It is just sad to see a once-proud cricket Test team lower than any I have ever seen before".