Ferrari's Vettel, 29, swore at Whiting over his team radio while duelling with Max Verstappen on the track.
The German, who won four world titles at Red Bull, later apologised.
But Horner said: "In any sport, you can't give abuse to the referee."
He suggested the sport's governing body the FIA would look at the incident, and added: "I would be surprised if that went unreprimanded."
Vettel was stripped of his podium finish in Mexico after he was ruled to have raced in a dangerous manner.
After switching to Ferrari from Red Bull in 2015, Vettel won three races and came third overall behind Mercedes pair Lewis Hamilton and Nico Rosberg. This year he is yet to win a race and lies fourth in the overall standings.
Both Horner and former Red Bull team-mate Daniel Ricciardo suggested Vettel's lack of success at Ferrari could have played a part in his outburst.
"It is not an attribute he had when he drove for us. Obviously his frustration he is vocalising, and everybody can hear that," Horner said.
"I definitely sense he has been a bit more frustrated this year," Ricciardo added.
Available FIA sanctions include a fine, or even suspending Vettel from the next race in Brazil.
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Red Bull team principal Christian Horner says he would be "surprised" if Sebastian Vettel escaped punishment for an expletive-filled outburst at race director Charlie Whiting during Sunday's Mexican Grand Prix.