"I got caught in the moment and took it too far," Stoinis said.
"I realised immediately I was in the wrong and I apologise to Kane and to the umpires.
"I did the wrong thing and accept responsibility for my actions. The standards are there for a reason and I accept the penalty."
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A sports diversity expert told the Sydney Morning Herald that the penalty wasn't harsh enough.
"Unless there are repercussions for people saying homophobic remarks, we're not going to get rid of them," Western Sydney University academic Dr Ryan Storr told the SMH.
Storr led a 2017 report on LGBTIQ inclusion prepared for Cricket Australia.
"Within the research I did, it showed that even at grassroots level it's still common to hear homophobic remarks.
"Across Australian sport, it's a bit all over the place, a bit inconsistent. Sometimes you get away with it, sometimes you get a three-match ban, sometimes you get a seven K fine. There's too much inconsistency and you need something a bit more solid to really show that it's not acceptable.
"Why any player would make those comments, especially in light of Israel Folau and the way that's going, you just know that's not acceptable," Dr Storr added.