The pair have criticised each other in the media in the past year following England's poor performance in the Ashes in Australia.
Lord Botham criticised the lack of preparation for Stokes's side ahead of last summer's Ashes, which led to Stokes calling him and his fellow former England skipper Michael Vaughan "has-beens".
England lost the series 4-1 amid off-field issues concerning late-night drinking sessions and breached curfews.
Botham, who scored 5,200 runs and took 383 wickets in 102 Tests, was asked whether he liked the way Stokes resigned as captain in the middle of a Test match against New Zealand in England.
"No, I didn't, and I stand by what I said," Botham said.
"You have got a situation, starting from the beginning when he had a go at myself and Michael Vaughan in Melbourne because we said they had not prepared properly.
"They played two-and-a-half days of cricket in the build-up to taking on Australia in Perth.
"But to be absolutely honest with you, we had a go at them saying that's ridiculous, no one knows what they are doing. The slip fielders have to practise. Very, very difficult."
When Stokes was asked by journalists for his views on the criticisms, he replied: "We've not been preparing for this tour over the last three weeks; we've put a lot of thought and process into this for a few years now.
"There's quite a few factors that play into why we can't prepare how the has-beens maybe prepared in the past."
Botham, who was part of two victorious tours of Australia in 1978-79 and 1986-87, was speaking at the Cheltenham Literature Festival to promote his new book, Seasons.
"So that's open warfare and I'm quite happy with that because I just think he let himself down," Botham said.
"He's a bloody good cricketer and he played well but he let himself down in those final couple of months.
"The team going 2-0 down in Australia, one of them in two days.
"For me, to be then seen at Noosa, one of the most popular places in Australia to holiday and, we have got five days off on the lash.
"I just thought that was poor. Curfews, well, they were set and they were broken.
"In the book, I just said that right at the end, a throw away line, 'Well, well, well, Ben Stokes, you are now a member of the has-been team'.
"Didn't go down too well, not that I'm bothered."
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