I'm an American who's been semi-seriously following world football for about 8 years now... and for me, all this folderol about Sterling needing to tell the referee that his trip was not a foul is... well... just that - utter folderol.
I've never ever, ever seen a single instance of a player - who having been awarded a foul - goes to the referee to disagree, stating that, in fact, no foul occurred. Out of curiosity, is there any recent (past 8 years or so) example of a player, from a top professional league, going to the referees after a penalty kick has been wrongly awarded in an attempt to change the penalty decision?
Anyhow, according to the announcers on BT Sport - even if Sterling had gone to the head referee - there would have been no change in the decision. Apparently - once the referee has ruled that a penalty has occurred, this cannot be retracted.
Thus, I'm utterly baffled by any claim that Sterling did anything dishonest/unethical.
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Moreover, it seems to me, that nearly any player in attack, while in possession of the ball in the opponent's penalty box, will go down at the slightest contact, or if anticipating contact, in order to draw a penalty kick - even if the contact is slight and isn't a rules infraction. Players not going down in such circumstances are subject to criticism if, by staying up and attempting to score/pass for a score - if, in these circumstances - a goal is not actually scored.
Given the above, what's the difference between going down after slight contact versus tripping - after which a penalty kick is awarded. Ethically I see no difference.
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To be clear - I hate diving and hope we can minimize/eliminate this from the game.
And, too, I'm in favor of ethical play. If Sterling could have altered the referee's penalty decision once the penalty had actually been awarded I think he should have stated that no contact occurred. Yet, had Sterling gone to the referees, the penalty award would not have been altered.
The super-ethical thing to have done - have Jesus intentionally miss the penalty under instruction to do so by the manager. But I've never, ever seen this happen in top league world football.
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TL/DR - Sterling did nothing wrong nor did our anyone in our side. A penalty was, unfortunately, wrongly awarded. We subsequently scored - as would have any other side in professional football.