The 35-year-old country singer has been married to his high school sweetheart Jessica Ussery since 2001 and has two daughters, 9-year-old Keeley and 5-year-old Kendyl.
Aldean told CMT Insider: "The main thing is that me and my family are okay, and everything's good there.
"I know everybody's kinda going to have their opinion, and for the people that know me and know what I'm about ... the people that are standing by us and supporting us, all I've got to say to them is thanks."
Aldean said that he is primarily embarrassed about the ordeal involving Brittany Kerr, and is grateful for the support he has received.
"I really appreciate it, and it's just been a really unfortunate thing," he added. "Really embarrassing, I think, more than anything."
Aldean said in a tweeted apology last week: "The truth is that I screwed up. I had too much to drink, let the party get out of hand and acted inappropriately at a bar."
Kerr also apologised for her part in the incident, saying: "The actions I portrayed recently were not a representation of my true character, but a lapse in judgment on my part."
Watch Jason Aldean performing 'My Kinda Party' on The Late Show with David Letterman: