Ryan Bertrand, Cole's understudy at Chelsea, failed to heed The Football Association's recent warnings about showing responsibility while using social networking sites when he swore in a tweet on Thursday.
"Sorry if i offended anyone by swearing as i don't encourage that type of language..." Bertrand later tweeted.
Bertrand wrote the expletive in a message that has since been deleted, after being forced to withdraw from contention for England's World Cup qualifier against San Marino on Friday through illness.
The incident came three days after Cole was charged with misconduct after insulting the FA with an obscenity in a Twitter message after the governing body questioned his evidence in a recent racism case involving teammate John Terry.
A series of off-field indiscretions involving England players has led to the FA writing up a new code of conduct that is set to be in place by next month.
Bertrand, who has played two matches for England, was moved to send his offensive tweet after clearly feeling the FA had failed to give a sufficient explanation of his illness, which was described as a sore throat.
"Just to clarify.... Its not a "sore throat" Im ill. swollen glands in my neck... And constant headache for 3 days now and freezin cold," Bertrand tweeted.
England manager Roy Hodgson said Bertrand will not be charged by the FA.
"His sentiments were laudable," Hodgson said, "but his choice of words was wrong. I'm pleased to see he has apologized for them."