Former Formula 1 title-winning team boss Briatore has been involved with Mark Webber's management throughout the Australian's grand prix career.
Webber lost the Malaysia win when team-mate Sebastian Vettel overtook him despite an order to hold station.
In an interview with Italian radio station RAI earlier this week, Briatore said Horner's handling of the affair had shown "weakness".
Briatore subsequently issued a statement saying his words had been "misinterpreted" and insisting he admired Horner's management of Red Bull.
"I have known Chris for many years and we have always enjoyed a great working relationship," Briatore said.
"Besides considering him a good friend, I have a lot of respect for him professionally.
"As a team principal, I think Chris has done an excellent job not only for Red Bull, but for Formula 1 in general, and he is still undoubtedly doing so."