The Tory leadership favourite acknowledged after speaking with Darroch that his comments in an ITV debate on Tuesday “would certainly have been a factor in his resignation”.
But Johnson claimed that was because the ambassador heard the comments second hand, and that they had therefore been “misinterpreted”.
His account conflicts with that of friends of Darroch, who have said the ambassador took the decision to resign after watching the debate, after which Johnson was accused of throwing the ambassador “under the bus”.
Darroch quit after it was revealed he had described the Trump administration as “inept”, “incompetent” and “uniquely dysfunctional” in Foreign Office memos leaked to the Mail on Sunday newspaper.
He was effectively blacklisted by Trump after the correspondence was made public.
Johnson spoke to the ambassador after his resignation.
Recalling the conversation with Darroch, Johnson told the BBC Andrew Neil in a leadership interview: “What he said was that somebody had relayed to him what I had said.
“(It) would certainly have been a factor in his resignation.
“I think that unfortunately what I said in that TV debate was misrepresented to Kim.”
Jeremy Hunt criticised his Tory leadership rival over the affair for the first time.
The foreign secretary, who was Darroch’s boss, told Neil he was “disappointed”, adding: “I think we have to back our diplomats all over the world.
“Sir Kim was doing his job. He was giving his own personal but totally honest view about the country he was serving in.”
Speaking on ITV’s Britain’s Next Prime Minister programme earlier this week, Johnson said he would pick the UK’s diplomats as PM, but declined to say Darroch would be allowed to keep his job.
“I think it is absolutely vital that the advice that civil servants give to ministers should not be leaked by ministers and should not be commented on by ministers if civil servants are going to feel free to give that advice with the impartiality that they want,” he said.
Pressed on whether Darroch, who was due to retire next year, could stay in post, he added: “It is vital that our civil service is not politicised by ministers leaking what they say. Whoever leaked that deserves to be eviscerated.”
Meanwhile, Hunt opened himself up to criticism from the eurosceptic wing of his party by failing to guarantee that Brexit would happen by Christmas.
He insisted he would deliver it sooner than Johnson because he was being realistic about potentially having to delay beyond the October 31 deadline to get a better deal.
But asked to rule out a delay beyond Christmas, he said: “I’m not going to give you those commitments because...getting stuff through parliament...I’ll tell you why - it’s because prime ministers should only make promises they know they can deliver.
“And there’s another reason we have to be careful about this October 31 date.
“It is because parliament may try and take a no-deal Brexit off the table altogether.
“I think I’m the best person to get a deal and if we get a deal it will be on or around October 31.
“But I can’t control what parliament does and that’s why I’m being honest with people about the difficulties.”
The separate interviews with both candidates will be broadcast at 7pm on BBC One.