The panelist had criticised Chmerkovskiy for taking "four eighths" to begin his instant cha cha cha with Brandy, which prompted a verbal sparring between the pair and host Tom Bergeron to joke: "Welcome to ballroom Smackdown."
Speaking on Tuesday's episode, the professional dancer apologised to fans for the incident and said he had "lost [his] cool a little bit" and would "go back to being cool" from now on.
When asked by co-host Brooke Burke if he had anything to say to Inaba, he replied: "Let's do our jobs. I'm trying to do mine."
Inaba also appeared to address the incident when she told the professional dancers that she had "always respected" their work on the show.
"You know, Maks, I just want to say something, first of all, to all the dancers, I've always respected all of you... so I hope that you will let it go."
Chmerkovskiy and Brandy fell into the bottom two on Tuesday night but were spared from elimination when Kurt Warner and Anna Trebunskaya were sent home instead.
The professional dancer later took to his Twitter account to thank fans for their support: "Crazy 'roller coaster' show this week! Thank u for keeping @4everBrandy and me dancing! Will be more 'politically correct' from now on :) (sic)"
Brandy added on her own Twitter feed: "Thank you so much for keeping @MaksimC and I in the competition!!! I was really scared tonight:( I appreciate all the love and support!!"
Dancing With The Stars continues next Monday at 8/7c on ABC.