Davies told Wednesday's Radio Wales Breakfast: "Deep down I think there were plans afoot as far back as April, because I was made aware of a plan to try and open the leadership question in April of this year.
"They would have picked up on anything to force a vote, and that's the right in a party to do that, because we live in a democracy, but I don't believe that the Conservative cause was helped by their plotting and their scheming."
MSs had raised their concerns, and according to Davies told him to quit, at a meeting last week, prompting Tuesday's vote.
He said the MSs had made three criticisms - on his messaging, "that I was indifferent to the job" and the recent attempt by his senior advisor to become Welsh Conservative chairman.
Nine Tory Senedd members, including Davies himself, backed him in the confidence vote, while seven were against him.
He told the programme there was a need to get the Welsh Conservatives "into the best possible place" to challenge the Welsh Labour government at the 2026 Senedd election and "make that change that Wales desperately needs"
"That was not going to be achieved with a divided group in the Senedd.
"The best way to unite the group, in my mind, was to tender my resignation despite winning the vote of confidence and ultimately allowing a new leader the best opportunity", he added.
Also on the programme, Millar praised Davies for leading the Conservatives in Cardiff Bay "with distinction for well over a decade".
He said he wanted build on his legacy and "get back to holding the Welsh government to account - that has to be our focus".
He was asked whether he would like there to be a leadership contest, rather than a "coronation" in which he would take the job unopposed, he said he would be "very happy to take on an opponent".