Webber confirmed on the eve of this weekend's British Grand Prix that he would leave F1 and Red Bull for Porsche's new Le Mans and World Endurance Championship programme next year.
Red Bull team boss Christian Horner was informed shortly before the news became public, having told reporters earlier this week that the door was open to the Australian staying on for 2014.
Webber revealed at Silverstone that his decision had been made "for quite a long time", but said he had no qualms about how the news was handled and had kept Red Bull founder Dietrich Mateschitz informed.
"It was a Porsche announcement, I informed Christian before the announcement which contractually I should do, and that is what we did," said Webber.
"It was about Porsche and Mark Webber today.
"I think I helped the team today; they have to make some decisions for the future.
"Dietrich has been completely up to speed with my thinking in the last few months, he has been on board, and encouraged me not to rush my decision when I approached him earlier this season.
"I think basically we went through all the right channels and avenues to get the message across and it was done in the right way."
Webber added that his commitment to his Red Bull F1 duties would not diminish now that he had chosen a future elsewhere.
"For the rest of the season it doesn't change a huge amount," he said.
"I have known the decision and nothing changes in my approach. In my last few races I'll be challenging for the top step.
"It's in my interests to keep the motivation up until Brazil, and to work hard with the guys.
"Given the effort that goes in to get the car there at this level, I need to keep pushing for myself and the team and all their efforts at the factory."
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