The England global said he was not surprised by the behaviour of the fans but did not elaborate on what was said.
In a post on Instagram, Sterling cited contrasting newspaper headlines about teammates Tosin Adarabioyo and Phil Foden buying houses."All I have to say is have a second thought about fair publicity and give all players an equal chance", he said.
Addressing the alleged abuse he received at Stamford Bridge, Sterling said that he "had to laugh" when he heard the remarks because he expects no better. He said the leg is the only thing he will ever shoot because his father was shot and killed when he was aged two.
And former England assistant coach Gary Neville revealed this week that Sterling complained during Euro 2016 of constant criticism from fans that carried racist undertones.
The 24-year-old England star has also been criticized for buying clothes at a high-street store and for buying his mother a house.
The PFA has been in contact with the England global to offer support and praised the restraint he showed at Stamford Bridge.
"But deep down, there was an understanding that there was a difference in tone to the attacks he was getting compared to others".
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CHELSEA fans have been warned bad behaviour will be acted upon at the Amex.
Chelsea boss Maurizio Sarri believes Man City are the best team in Europe, despite seeing his side hand the reigning Champions their first Premier League defeat of the season last night at Stamford Bridge. What I like is that 95 percent or more of the people are not like this, so we should try to find the right amount of tension for these people.
Are FIFA? Are they doing enough?
English soccer's players' union said Sterling was "often singled out and treated more harshly than his colleagues".
A Chelsea spokesman said: "We're aware of reports and video footage".
"You think in football we'd be safe, but racism is everywhere". That is how it is.
The flashpoint in City's weekend match came when Sterling went to collect the ball for a corner and was berated by Chelsea supporters leaning towards the advertising hoardings, including one man who appeared to use a racial slur. We've got to take the positives out of the game, and there were so many more positives than negatives.
"Yes, punish them but do not talk too much about them because they do not deserve that we talk about them".