In an interview with The Guardian, Whelan is reported to have said there was not "a lot wrong" with anything Mackay - appointed Wigan manager on Wednesday - had said in abusive text messages currently under investigation by the Football Association.
As well as prompting widespread criticism, Whelan's comments followed one of Wigan's kit sponsors ending their association with the club over Mackay's appointment.
A statement from anti-racism campaigners Kick It Out questioned whether the 77-year-old was a "fit and proper person" to be running a football club, something Whelan was quick to dismiss.
"I would strongly object to that [Kick It Out's claim]," he told Sky Sports News. "I have played football in all four divisions. I have had massive experience in football.
"I brought Wigan Athletic from the fourth division to the Premier League, and we won the FA Cup.
"I fight to get Wigan Athletic to do well, I have a reputation and I don't want it tarnished."
Whelan made references to Jewish people "chasing money more than everybody else" and also brushed off a derogatory term used by Mackay about Chinese people – drawing stinging criticism from both communities.
On the subject of anti-Semitism, Whelan added: "I would never insult a Jewish person. I have got hundreds and hundreds of Jewish friends. I hold them in the highest regard.
"If anyone takes offence please accept my apologies. I did not mean to insult any single person.
"I have got loads of Chinese friends. I would never insult the Chinese."
Earlier on Thursday, having condemned Whelan's actions, Kick It Out called for the FA to fully investigate the comments made by the Wigan owner.
The statement read: "The Football Association has outlined in a statement that 'no assurances have been given on the outcome of the case' yet Wigan Athletic owner Dave Whelan continues to suggest elsewhere that two 'influential' people have informed him that 'nothing will come' from the investigation.
"He has brought into question whether he is a fit and proper person who should be running a professional football club.
"The remarks act as another example of the culture which continues to exist within football, and further proves that some in positions of power seem comfortable sharing those views either privately or publicly.
"These comments must not go unchallenged and have to be investigated by the FA."
