Mark Webber's win at Sunday's British Grand Prix, secured with a brave move on Ferrari's Fernando Alonso with four laps to go, was Red Bull's third of the season and moves the Australian within 13 points of the Spaniard in the race for the title.
Webber's team-mate Sebastian Vettel was third to give the team a first double podium of the year, following on from a dominant display in Valencia where only an engine failure denied the two-time world champion a certain victory.
With Red Bull having been the pacesetters on two very different circuits in Valencia and Silverstone, there is a concern that they have stolen a march on their rivals, with only Ferrari seemingly able to match them.
The Milton Keynes-based squad now hold a handsome 64-point lead at the top of the constructors' championship, but Horner said: "I think it is far too early to write off anybody in this championship.
"If you look the two most consistent finishers (Alonso and Webber) are leading the championship so finishing races is critical and you can't write off any of the major contenders.
"There is a lot of racing still to do at a lot of different circuits.
"We had a strong weekend which made up for what happened in Valencia but I think it is far too early to write off anybody."
While Red Bull enjoyed an excellent weekend, it proved a miserable experience for McLaren as their predictions of a strong showing were proved wildly inaccurate.
The MP4-27 struggled for speed, leaving Lewis Hamilton and Jenson Button only able to manage eighth and 10th place finishes.
Hamilton now lies fourth in the championship, 37 points adrift of Alonso, with Button a massive 79 behind in eighth, while McLaren dropped to fourth in the constructors' standings behind Lotus.
But Horner remains wary of the Woking marque.
"It would be dangerous to write anybody off at this stage," he said.
"We are doing okay but there are a lot of drivers in contention.
"It has looked like a pattern has been emerging at the last few races but that could be thrown out of the window quite easily at the next race."
Vettel and Webber's relationship became strained as they battled for the title in 2010, but Horner does not envisage any similar issues this season, even though the pair are separated by just 16 points.
Horner said: "They have spent a lot of time racing each other and they have spent hundreds of hours together working on developing the car and I think they have a genuine respect for each other.
"Sebastian knows in Mark he has a very genuine competitor, and Mark knows Sebastian has been the benchmark for the last couple of years.
"It's a healthy situation for the team. I think they now have more experience."