Rixon's role on the Australian team coaching staff came to an abrupt end on Wednesday, when it was announced his services were no longer required.
The former Test wicketkeeper said his departure was not completely unexpected, reiterating he was always going to step away before the IPL starts in April.
Rixon maintained he had no issue with coach Darren Lehmann's decision to cut him and restructure his staff, but he said he had "little respect" for Cricket Australia.
"I'm not getting into a slinging match ... I have very little respect for the organisation, so I think we best just leave it there," Rixon told Sky Sports Radio on Thursday.
"I don't like a lot of things they do. They interfere basically with a lot of the cricket decisions over the period of time and I don't necessarily agree with that.
"It's none of my business. At the end of the day, I do what I do, I go out and do it to the best I know how.
"But it's probably just draining and the one thing I've lived my cricket life with is a major passion for the game."
Asked whether Howard - a former rugby union player, coach and high performance boss - was the interfering CA staffer he was specifically talking about, Rixon said: "Let me say, I hope he was a good rugby player."
However, Rixon said Lehmann and captain Michael Clarke were well-placed to run their own ship and ignore outside voices.
"With Michael now being very content with where he is, Boof's obviously come in with a stronger approach to that," he said.
"That's why I think cricket's in a very good shape with Australia, we're starting to get all those bits and pieces (together).
"Darren will eventually get a team around him that he's very, very comfortable with and that's fine. That's the way life is, that's the way it is with coaching."
The 59-year-old will again work with the Chennai Super Kings and hopes to pick up a gig with other Twenty20 teams down the track, including in the Big Bash League.
Rixon said Australia should follow the lead of other countries and make national T20 coach a separate job to Test and ODI coach.
"There's been a lot of impersonating a man talking to himself. Because five years ago I suggested that. It was a good idea then and is still a good idea today," he said.
"T20 should be segregated as a different identity to the other two brands of cricket. It just makes sense."