Larkham, Australia's attack coach since 2015, was the high-profile fall guy of Rugby Australia's review of the Wallabies' worst season in 60 years in 2019.
The Wallabies won just four of 13 tests, with all the coaching staff including Australia's 1999 World Cup hero Larkham, in the firing line.
Cheika's soul-searching over what to do next led to his proposal to axe the former Australian first-five, as well as "four or five others".
"Tough," Cheika told an Irish sports podcast in Dublin of his decision to dispense with Larkham.
"For a friend, maybe not anymore, I'm not sure.
"But one thing's for sure: I don't blame anyone for anything."
Crowned world coach of the year in 2015 after teaming with Larkham to take the Wallabies to the final of the last global showpiece, Cheika said he never doubted his own ability as Australia's head coach after last year's poor performances.
But he asked himself: "What am I going to do?"
"More challenging myself as to what will be the thing I do now to make the change?" Cheika said.
"And after the season I spent a week really detailed, just myself, going through - removing the emotional connections - and going through exactly what I needed to do to make sure that this season was bright and more enjoyable and that we don't live the peaks and troughs.
"(That) we just build and build and build until we get to where we want to go."
Cheika said he had to balance taking responsibility, protecting people and at the same time "shake it up a little bit".
"So (it was) very tough but I just think that sometimes you've got to make those (decisions). It wasn't just him," Cheika said.
"There were four or five others that we made changes to in the team and I'm sure that when we go to the World Cup the team will be in the right position and feeling the right way, partly because of some of those changes of what's come in and what we've needed to change."