The Englishman also insinuated the cause of the issue was a "rogue marshal" and further suggested the FIA should have better control over its garrison of volunteers.
The FIA summoned Horner to the stewards for a breach of the International Sporting Code for misconduct towards officials.
That has resulted in the slap on the wrist, with Horner to also take part in an FIA Stewards' Programme next year.
A stewards' report read: "He explained that his reaction was one that was made under the pressure of competition following the penalty imposed on the driver of car 33.
"The stewards explained that the marshal concerned was doing his job in precisely the manner prescribed in the International Sporting Code.
"Mr Horner offered to apologise to the marshal concerned and to explain to the media
that he meant no offense.
"He also offered to participate in the 2022 FIA International Stewards' Programme in
early February.
"The stewards unreservedly accept Mr Horner’s offer."