Red Bull design chief Adrian Newey spent the Belgian Grand Prix worrying about the safety of drivers Sebastian Vettel and Mark Webber because of tyre problems.
Red Bull, who recorded a 1-2, had asked to change tyres before the race because of blistering sustained in qualifying.
Newey told BBC Sport: "It was one of the scariest races I've been involved in. It was heart-in-the-mouth stuff."
Tyre supplier Pirelli said tyre damage was partly caused by Red Bull.
"We've never had a safety issue," said Pirelli motorsport chief Paul Hembery, who said the damage was caused by the lack of running on Friday because of wet weather and taking the tyres to the limits of their recommendations.
That is a reference to the amount of camber - or lean away from vertical - that Red Bull run on their tyres.
Pirelli's recommended maximum camber is four degrees but Newey revealed that the camber on the Red Bulls had been "just a hair over four, four and an eighth, or something, just a tiny bit over".
Newey added: "Obviously if we had known there was a safety concern about it, we wouldn't have done it.
"We had some dialogue with Pirelli about it (before qualifying) and they didn't seem concerned, but after qualifying if you change it without (governing body) the FIA's blessing you have to start from the pit lane.
"Pirelli were telling us after qualifying that our tyres were very marginal and they wouldn't say whether it was after half a lap or five laps, but they were going to fail.
"Tyying to make that call in making sure the car was safe, while not handicapping ourselves from a performance point of view, was quite a difficult judgement to make. Frankly, at the end of the race, I was very relieved that both our drivers were safe."
It is against the sport's rules to change the tyres of those drivers in the top 10 after qualifying but Red Bull had hoped to win special dispensation to do just that before the race started.
However, rival teams objected on the grounds that Red Bull were responsible for creating the problem and therefore they should find their own way around it.
After Pirelli and FIA race director Charlie Whiting discussed the situation, Whiting decided to refuse Red Bull's request.
That left the defending constructors champions with the decision as to whether to change the camber on the wheels, which would have meant starting from the pit lane, or increasing the tyre pressure - which lessens the risk of tyre failure - and making an early pit stop.
Newey said the team calculated that, by increasing pressure, Webber's tyres would last until lap two or three and Vettel's until lap five.
Webber eventually stopped on lap three for fresh tyres and Vettel on five, before the German went on to lead his team-mate home ahead of McLaren's Jenson Button and Ferrari's Fernando Alonso.
Hembery said: "If you were concerned there was a safety issue with your set-up creating issues with the tyres you could have started form the pit lane, put a new set of tyres on, change your geometry and off you go."
BBC Sport understands some rivals are unhappy about Red Bull's decision to exceed Pirelli's recommendation on camber and that a tougher stance may be taken at the next race, the Italian Grand Prix.
The blistering - where the tyre oveheats and bubbles - occured close to the inside shoulder of the front tyres, where the sidewall meets the tread.
Red Bull were not the only team to suffer from the problem. McLaren's Lewis Hamilton and Toro Rosso's Jaime Alguersuari also struggled after qualifying, while Fernando Alonso's Ferrari suffered during the race.
Italy's Monza track, which stages the next race on 11 September, features a series of long straights and has traditionally been one of the circuits where this issue is most likely to occur.