However, the Tory leadership frontrunner denied failing to give Sir Kim his backing and said his words during a televised leadership debate had been “misrepresented”.
Mr Johnson’s lack of explicit support for Sir Kim during the ITV debate on Tuesday was widely seen to have been the final straw for the envoy following the leak of his diplomatic cables criticising Donald Trump’s White House.
Furious Tory MPs accused the former foreign secretary, who is favourite to succeed Theresa May, of throwing Sir Kim “under a bus”, leaving him no option but to resign.
But in an interview with the BBC’s Andrew Neil, Mr Johnson said when he spoke to Sir Kim by telephone the ambassador told him he had not seen the debate himself although somebody had told him about Mr Johnson’s comments.
“He said that what somebody had relayed to him had been a factor in his resignation,” Mr Johnson said.
He added: “I think that unfortunately what I said on that TV debate was misrepresented to Kim.”
His rival for the leadership, Foreign Secretary Jeremy Hunt, said Sir Kim had made it clear that Mr Johnson’s comments were a factor in his decision to quit.
“He’s been clear that that was one of the factors and I think it’s a great shame,” Mr Hunt said in an interview with Mr Neil.
Mr Hunt said he had been “disappointed” in Mr Johnson’s response during the debate when he tried to pin him down on whether he supported Sir Kim following a furious tirade against the ambassador from Mr Trump.
“We have to back our diplomats all over the world,” he said.
“Sir Kim was doing his job. He was giving his own personal, but totally honest, view about the country he was serving in.”
Meanwhile, Mr Trump has suggested that he was too quick to denounce Sir Kim following the leak of his diplomatic dispatches in which he described the White House administration as “inept” and “dysfunctional”.
In a trademark Twitter outburst, the president described Sir Kim as a “pompous fool” and a “very stupid guy”, leaving the ambassador to conclude that his position in Washington had become “impossible”.
However, speaking to reporters at the White House, Mr Trump said he had since been told Sir Kim had said “some very good things” about him.
“I wish the British ambassador well. Some people just told me - too bad - they said he actually said some very good things about me,” he said.
“I guess I quoted (Republican Senator) Lindsey Graham today. He said some things that were pretty nice from the British ambassador.
“I wish the British ambassador well but they have got to stop their leaking problems there just like they have to stop them in our country.”
Mr Graham, an ally of Mr Trump, said he believed Sir Kim had had a “raw deal” from the press, with “selective” coverage of his cables.
“Kim Darroch did an outstanding job as ambassador and sorry to see he has resigned his post,” he tweeted on Wednesday.
“Ambassador Darroch always understood the strength of President Trump and referred to him as the ‘Terminator’ who is indestructible and will most likely be re-elected.”
There will be relief in Whitehall that the row over Sir Kim’s cables appears to have had no lasting impact on relations with the US, coupled with concern that his resignation may have been unnecessary after all.