Azaria said he spent the better part of a year "doing the work", in which he "read, spoke to people who knew a lot about racism, spoke to lots of Indian people and went to seminars".
"I realised I have had a date with destiny with this thing for 31 years."
Azaria, who voices a range of other notable characters in the series, including Chief Wiggum, Moe and Comic Book Guy, said Apu was created with only good intentions.
"I really didn't know any better. I didn't think about it. I was unaware how much relative advantage I had received in this country as a white kid from Queens.
"Just because there were good intentions it doesn't mean there weren't real negative consequences to the thing that I am accountable for."
Initially, the show's producers tried to laugh off complaints, which were sparked by the documentary The Problem With Apu by Indian American comedian Hari Kondabolu.
But in February this year, The Simpsons creator Matt Groening told BBC Radio that he was "trying to make it better".
"Bigotry and racism are still an incredible problem and it's good to finally go for more equality and representation," he said.
Show producers are now in the process of recasting all of its non-white characters who are currently portrayed by white voice actors.
Among them is Dr Hibbert, who until now has been voiced by Harry Shearer, set to be replaced by Kevin Michael Richardson.
Apu will return when a new actor is cast.
Azaria also addressed countercriticism that his stepping down sparked from those who describe it as "cancel culture" or "over-sensitivity".
"I have people say to me, 'Oh does this mean you can't play Wiggum because you're not a real cop?' That's just ridiculous.
"If it's a character of colour, there's not the same level of opportunity there. The first argument is, if it's an Indian character, Latin character or Black character, please let's have that person voice the character.
"It's more authentic, they might also bring their experience of their culture to it – and let's not take away jobs from people who don't have enough."