Balotelli exchanged jerseys with Real Madrid defender Pepe at half-time of Liverpool's 3-0 UEFA Champions League defeat at Anfield on Wednesday.
The striker's decision provoked criticism in some quarters, and Rodgers himself stated in the immediate aftermath of the game that he would deal with the issue.
But during Thursday's media conference ahead of Liverpool's Premier League meeting with Hull City at the weekend, Rodgers refused to divulge any details of his discussion with the Italian.
"Any action would be kept within ourselves," he said. "It was just a conversation that that's not the culture in this country or at Liverpool. That's the matter closed."
Balotelli's record of one goal in 10 Liverpool appearances has also attracted criticism, and Rodgers accepts that such scrutiny is part of the modern game.
"There'll be that of course," he added. "It's one where the boy is trying very, very hard. Longer term, we'll see how that works out for him but certainly he is working hard on the training field to improve his opportunities to play in the team regularly and to score goals.
"As long as he's doing his best that's all I can ask. Whether his best is good enough remains to be seen, but that goes for any player.
"Is this the Mario Balotelli press conference?" Rodgers said when quizzed further on the Italian. "He's like every other player. He wants to score and obviously at this moment in time he's not. Hard work will improve confidence and when you're confident you'll have more success.
"The 'Mario Balotelli show', like you say, is no different to me. He's treated like any other player, for me as a manager it's been no problem.
"I like players that are different. People talk to me about boots and hair and I like that individuality - as long as they fit in with the team."
