Asked about this, Horner said: "I don't think either driver is going to stick their hand up and say 'yes, it was all down to me'. As Mark has said, both drivers will go to their graves with differences of opinions.
"We got the drivers together, sat down with Adrian [Newey, the chief technical officer], with Helmut and we had a very positive and constructive meeting.
"Mark is one of the hardest guys in grand prix racing, he's is a tough racer, a tough competitor.
"He's mentally very strong and he's in the form of his career at the moment and he won't give a quarter, and arguably the person you least want to be overtaken by is your team-mate.
"I think both drivers recognise from a team point of view that it was a disastrous outcome.
"They were sorry for the team, the body language between them was very relaxed because they are good team-mates, they work well together and they have raced each other successfully wheel to wheel on several occasions and an incident like this we won't allow to disrupt that relationship."
Red Bull's response in the immediate aftermath of the accident has strengthened a widespread belief that the team favour Vettel and has led to conspiracy theories that they were trying to engineer a win for him.
But asked about reports that he had told Webber's race engineer to order the Australian to let Vettel past, Horner said: "I don't think I actually said 'move'.
"I don't talk directly to the drivers until after the race. Mark's engineer had no instruction to tell Mark to move out of the way - 100% clear."
He added: "There was no conspiracy trying to get one car past the other or getting one to slow down.
In-depth interview - Sebastian Vettel
"We were allowing both drivers to race and I don't think that is wrong. What I do believe is wrong that they unfortunately drove each into each other!
"Red Bull is about racing, it's not about processions, otherwise we would have given team orders after the first turn or the pit stop.
"We had two guys that we are trying to give equal opportunity to win the world championship and win races being heavily pressured by the McLarens."
Horner said it was likely the two drivers would be racing hard against each other again at this weekend's Canadian Grand Prix.
But he said he expected Red Bull's comparative lack of engine power to make things difficult on a track that features a lot of long straights.
"This weekend represents one of our biggest challenges of the year," he said.
"The next two races in Montreal and Valencia our horsepower is heavily weighted. We know we have a deficit to the benchmark engine in F1.
"If we can be quick in Montreal we have nothing to fear between now and the end of the year in terms of circuits.
"But we have some mighty opposition. Sometimes you have to pinch yourselves - in a short space of team this team is beating and competing with the likes McLaren and Ferraris which would have been unthinkable over the last two years."
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