The PEOPLE Country cover star, 35 – who apologized last week after being photographed getting rather cozy with American Idol contestant Brittany Kerr – says that he's primarily embarrassed about the ordeal, but he's grateful for the support he's received.
"The main thing is that me and my family are okay, and everything's good there," Aldean told CMT Insider.
"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," he said.
"I really appreciate it, and it's just been a really unfortunate thing. Really embarrassing, I think, more than anything," he added.
Aldean has been married to his high school sweetheart Jessica Ussery since 2001 and has two daughters Keeley, 9, and Kendyl, 5
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Kerr also apologized for her part in the scandal.
"The actions I portrayed recently were not a representation of my true character, but a lapse in judgment on my part," she said, as reported by TMZ.