The Milton Keynes squad cemented their place in the Formula 1 record books in 2012 by becoming just the fourth team in history to win three Constructors' Championships on the spin, with star driver Sebastian Vettel also clinching his third straight drivers' title.
Their sustained run of success means Red Bull will inevitably start the forthcoming campaign as the favourites for both championships again, with their initial preparations having got off to a trouble-free start at the Jerez test last week.
And speaking to Sky Sports F1's Natalie Pinkham in an exclusive interview for The F1 Show, Horner admitted, that while their thirst for further titles is undiminished, the team's recent title haul had inevitably lifted some of the pressure from their shoulders.
"In many respects the pressure is off us because we've achieved a triple double World Championship," he said. "Nobody can take that away from us, that's in the history books.
"But we put the pressure on ourselves because we want to continue that run of success. Of course, going into the season as reigning champions, you're there to be beaten, you're there to be shot at. But it's something we've got used to over the last couple of years. Pressure is part of this business, it's part of this sport.
"But in many respects we go into 2013 more relaxed than previous years because of what we have achieved. I think the team has continued to grow and continued to evolve and we're in a good position to deal with that pressure."
Indeed, he made clear that Red Bull have no intention of easing off in 2013 and are determined to maintain that winning feeling.
"It's a big thing [winning three title doubles in as many years], but motivation is sky high," Horner added.
"We're still a relatively young team and everybody enjoys winning. They enjoy the success and there's a real determination. Formula 1 is the biggest team sport in the world and you only win races and championships by having all of the departments working cohesively together.
"We've got great strength in depth here, great character in the team and my role is to make sure we're getting the best out of all areas, everyone knows what the targets are and everyone's delivering what's expected."
Although the world champions' start to winter testing has begun encouragingly - and both Vettel and Mark Webber have declared that the new RB9 is in better shape than the RB8 was at this same stage 12 months ago - Horner reveals he had been prepared for the 2013 challenger to make a delayed introduction.
"It's tough and it's been very tough for the design and production guys," he replied when asked about the winter schedule.
"The battle in 2012 went all the way down to the last race, so we were developing the car all the way up until Brazil.
"It was the latest start we'd ever had and when Adrian [Newey] comes into your office and says 'I think we're running a bit late on the new car' - he's not known for being early at the best of times!
"So it's been an amazing effort over the winter period, over the Christmas break in particular to have got the car ready for the first test. Only time will tell if it's enough."
But as has become common practice in F1, the Team Principal added that the 'evolutionary' RB9 would still feature a number of significant changes come the first race in Australia in a month's time.
"The car's always a prototype, so the car that ran in Jerez last week will be quite different in Melbourne," Horner said.
"But that's the same for certainly most of the front-running teams. The pursuit of development will be relentless and will certainly be a key factor in this year's championship. But with the regulations being stable, you get into the law of diminishing returns. The gains you can make aren't quite as big as they were perhaps three of four years ago. So therefore the devil does tend to be in the detail."