"Very hard to manage the tyres, lot of blistering, but we manged to hang on", he said. "In front of all the fans at the Red Bull Ring and in a Red Bull".
Meanwhile, Vettel now leads the Drivers' Championship by a single point ahead of next weekend's British GP at Silverstone, with Ferrari also nudging ahead in the Constructors' stakes amid their rivals' horror show.
It compounded a software miscalculation that cost Hamilton a win in Australia and the very similar decision not to pit him under the safety auto in China that led to a Red Bull victory for Daniel Ricciardo.
It was a dream start for Mercedes, with their championship leader ahead of team-mate Bottas, and Vettel back down the order after his grid penalty.
"I couldn't have chosen a better race to do it, so very happy", the Dutchman, cheered on by an estimated 20,000 countrymen in the crowd, added. "A positive day but it could have been better". However, the auto was very good, we had a very good pace and we didn't have any issues with the tyres; in fact, the vehicle was very good on them, even if I had to manage the Softs for a long stint, which again proves we have made good progress since Barcelona.
"Eight seconds? How did we miss that". In all 33 Grand Prix since then, Hamilton had finished inside the points and set a new record for consecutive points finishes.
Bottas was also cautious, noting that the upgraded engine didn't drastically increase Mercedes' advantage in France.
"My gearbox is gone", he told the team. The team's fifth major error in only nine rounds this year left Hamilton in no-man's land.
On a bleak afternoon for the champions, who had not been beaten at the Red Bull Ring since Austria returned to the calendar in 2014, Hamilton's team mate Valtteri Bottas retired with a mechanical failure.
Portugal-Uruguay clash more than Ronaldo, Suarez - Alves
Gelson Martins and Raphael Guerreiro are both in contention to start having returned to full training following injuries. They soon followed it up with another 1-0 victory over a determined Saudi Arabian side with help of a Luis Suarez goal.
"It's my mistake. Do what you can", replied Mercedes strategist James Vowles.
In came Hamilton for tyres on lap 25.
"Obviously I was saving tires, pushing at the same time, you never know. I'm sure the guys will be working to rectify things".
It was clear that tyre wear was emerging as a critical factor. But I think the pace was very good, the tyre management was very good.
On lap 53, he pitted again for super-softs, dropping a place to fifth behind Ricciardo, who nearly immediately slowed and stopped.
With Ricciardo out of the race, Hamilton was back up to fourth, only for his race to end before the chequered flag as well due to a loss of fuel pressure. Sebastian Vettel (GER/Ferrari) 3.181,4.
Between the two sessions, Haas F1 Team ran a total of 133 laps - 69 by Grosjean and 64 by Magnussen. Starting from the pitlane, McLaren's Fernando Alonso ran as far as 19th in the early laps, only to finish eighth with the VSC and a late charge helping the cause. Marcus Ericsson (SWE/Sauber-Ferrari) one lap, 11.
Williams driver Lance Stroll, who did a good job to make Q2 for the first time since the Azerbaijan Grand Prix two months ago rounded out the top 15. Stoffel Vandoorne (BEL/McLaren-Renault) three laps.
Horner also paid tribute to his team for pulling off a high-pressure double stacked stop during the virtual safety vehicle period that was called when Valtteri Bottas retired.