Bates enjoyed 22 years in charge at Stamford Bridge before selling up to Abramovich in 2003.
Bates told thelondonpaper.com: "When Roman Abramovich came in he knew nothing about football, he's more interested in making money.
"They haven't treated the supporters very well. They've jacked up the prices so much they've alienated the real fans.
Bates also believes Abramovich has made a mistake by sacking Jose Mourinho.
He added: "If you appoint football men you've got to let them get on with it.
"I was never a fan of Mourinho personally but you can't deny he gets results.