He said yesterday's show had aimed to "understand better what is a very complex and sensitive issue".
"We have no problem apologising to Amy for any offence," Mr Jackson said. "I thought that we had been sensitive with her yesterday, maybe we could have done a better job."
He said they had the "utmost respect" for Amy for speaking out about the issue and praised her "bravery".
The audio from the interview has since been removed from the RadioLive website, and comments on the page were closed last night.
The pair spent almost the first hour of their daily show talking about the interview and their handling of it, with listeners calling in to give their opinions.
Among a mixture of support and criticism about their questioning of Amy, Mr Jackson admitted that he listened back to yesterday's interview himself after seeing some of the negative feedback.
"I listened back it because I thought, 'what the hell are these people talking about?' ... and I think we could have done it better,'' he said. "But I think people can take things out of context in a 10-minute clip, because I thought it was a great three hours yesterday and very balanced.''
Mr Tamihere also levelled some criticism at the media reporting of the interview, saying "there's a bunch of people in the media that hate our guts''.