Sterling, now with Manchester City, signed a contract on December 21 2012 aged just 18, which saw his wages reportedly rise from £2,000 to around £40,000.
"There is one common denominator when it comes to young players falling by the wayside - money," Celtic boss Rodgers told the Daily Express.
"I couldn't do it any longer than about the November time because he was absolutely brilliant, so we had to get him on a different contract.
"But I stretched it out as long as I could.
"With young players, one, they have to earn it and, two, you don't go overboard with them because they have played a couple of good games."