Horner said: "Under my leadership, I have led the team to those 35 victories and [six] world championships.
“Has he learnt from it? I'm sure he has. Is my leadership undermined? I don't think so”
Christian HornerRed Bull team principal
The 39-year-old does have an impressive record at the team since its debut in 2005, overseeing three drivers' championships and three constructors' championships.
He added: "Of course there have been lumps and bumps along the way. There have been incidents between the two drivers but we retain them because they are both fiercely competitive individuals.
"They drive each other forward and bring the best out of each other. I think it's a healthy rivalry.
"In that race he didn't do as I asked. Was I happy about it? Of course I wasn't. Did we discuss it? Yes we did. Did he apologise? Yes.
"Has he learnt from it? I'm sure he has. Is my leadership undermined? I don't think so. Would he do it again? I think he'd think twice, but as he explained yesterday there is history between those two drivers.
"It is not something new, it is something that has been there for four or five years. Let's not forget they are one of the most successful pairings that the sport has ever seen."
Vettel: I would ignore orders again
Horner also denied claims that Vettel thinks he is above the team, however, he added that the German has not got where he is today without making big decisions.
"I don't think Sebastian for a moment thinks he runs the team," he said. "He knows what his job is, he knows what we employ him to do and he knows why we employ him to do it.
"He's been with Red Bull for a long time now. He recognises more than anybody the value that the team has behind the success he has had.
"He knows he can't operate without the team so he doesn't put himself above the team for one moment. He has made a decision in a race as a hungry driver who based his decision on all kind of emotions at that time.
"Seb has not achieved the success he has in his career by being submissive. He saw an opportunity, he had saved a set of tyres and he wanted that victory more than anything else."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.