However, the rush of excitement he got in the aftermath of that first triumph back at the 2009 Chinese Grand Prix helped drive him and his staff to want to deliver more and more success in F1.
Max Verstappen’s triumph in last weekend’s Canadian GP was Red Bull’s 100th victory in F1 and put it now fifth in the standings of F1’s all-time winners.
Of the four squads ahead of it, Ferrari leads the way on 242 victories, ahead of McLaren on 183, Mercedes on 125 and Williams on 114.
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Reflecting on the journey to those 100 wins, Horner confessed that the first victory in Shanghai felt like such an achievement at the time that it was almost like Red Bull’s mission in F1 had been completed.
“When we first came into the sport, the ambition was to be competitive and to compete,” said Horner. “It was Dietrich's [Mateschitz] vision to bring Red Bull in as an entrant. And not just take part but try and be competitive.
“We won our first race in 2009, four years after coming into the sport. I remember collecting the trophy that day and then getting on the plane to go home that evening and thinking, ‘Well, at least we've won one. If nothing else happens, we've won a race!'
“But it felt so good that it was like: ‘Well, we really want to feel that again.’ And who would have thought 99 victories later we would achieve a century. So, it's a landmark for the team.
“It's testament to the dedication and the hard work of all the people within the company, both trackside and behind the scenes, plus all the support services.
“There's so many unsung heroes that have contributed to this incredible achievement. So, it's something that the whole team is incredibly proud of.”
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Horner praised the attitude that former owner Mateschitz, who passed away last year, had when he originally laid out his ambition to enter F1.
“He wanted to do things differently,” said Horner. “He wanted to be different. He didn't want to be a corporate team, where you needed 25 passes to get into the motorhome.
“So, he introduced the Energy Station. He introduced the Red Bulletin, and he wanted it to be fun. But he was also competitive. He wanted to compete, and he wanted to win.
“He was a racer. He was a fan of Formula 1 and passionate about the sport. And, of course, F1 for him and for Red Bull was a great way of marketing the brand and the product.”
Asked by Autosport what he felt had been the key characteristic that had helped turn Red Bull into such a successful team, Horner said: “It's the people, it's the spirit, it's the culture.
“It's the attitude that we have. It is the way that we go about racing. It is the desire. It's the passion. It's the commitment. It's all of those aspects.
“When you work for a team like Red Bull it's clear what our goal is. It is that we want to win, and we want to be competitive.
“Everybody gives their best, and they buy into that. You feel that energy in the factory. It's a culture that we have which is different to other teams. It's a racing team. It's just a big racing team.”
Additional reporting by Adam Cooper