Sterling agreed to do an exclusive interview with the BBC last week and defended himself for rejecting Liverpool's contract offer of 100,000 pounds per week.
The 20-year-old made it clear that he was "no money grabber" and added that Arsenal's interest in him was "quite flattering".
However, Rodgers was seething about the fact that Sterling was allowed to conduct the interview just a few days prior to the match against the Gunners.
"You are not a 20-year-old boy and you pick up the phone and ask to speak to the BBC," Rodgers said during a press conference. "You don't do it. Him in particular. But, of course, if he is asked to do that by other parties then that is what he'll do.
"In the modern game it's something that would frustrate us all. It's the market. In fairness to Raheem, I brought Raheem in from the youth team so I know the kid well and I know a big part of this is nothing to do with him. He's a kid who is focused on his football, works hard every single day, he just wants to play his football.
"The kid gives me everything every time he trains and plays. Loyalty is not something so prevalent in the modern game."
Despite Sterling refusing to sign a new contract, Rodgers insisted that the forward will be staying at Anfield.
"I had a good chat with him and given my opinion on it," he said. "The only thing I will say on Raheem's situation is anyone can see through his football development, and financial, Liverpool Football Club is the best place for him.
"He has had the opportunity to play, which is key for a young player. It's the model of Liverpool, the owners want to create world-class talent. He came in at 17 years of age, I deemed him worthy to come in and become a regular.
"In two and a half years he has proven that. He has played in a number of different positions, which has improved him tactically and technically."