The married singer was recently photographed kissing former American Idol star Brittany Kerr and later apologised for acting "inappropriately".
Aldean, who has said that his family is "okay" after the incident, has now described the encounter as "unfortunate".
"When it comes to fame, obviously you take the good with the bad," he told E! Online.
"Family's good, we're working through it. We're trying to move on - that's the biggest thing. And hopefully people will allow us the privacy to do that - and that's kind of it."
Kerr has reportedly been offered a reality show following the scandal, although the rumours claimed that she was unlikely to accept the proposal.