The Australian's closest rival heading into the race, Lewis Hamilton, failed to finish after a collision between the two and Webber said he had done as well as he could have hoped for.
Formula One leader Mark Webber was pipped by championship rivals Fernando Alonso and Sebastian Vettel at the Singapore grand prix on Sunday but appeared the happiest of the three at the end of the floodlit race.
The Australian's closest rival heading into the race, Lewis Hamilton, failed to finish after a collision between the two and Webber said he had done as well as he could have hoped for.
"Waking up this morning I would have been happy with third," Webber told reporters.
"I am very happy -- this was the toughest weekend of the year for me. I didn't feel comfortable all weekend. To get third place out of it... It is easy to panic so I had to stay composed
Starting the race in fifth place, Webber gambled on an early pit stop during the first safety car period after three laps and worked his way through the field.
"I got caught up a bit, Lewis got a big run on me. There was contact and it's not something you want to do all the time," Webber said of his collision with Hamilton, before praising his team for the pit-stop strategy.
"I thought 'I am not sure about this' -- I questioned the team to start with and they said it''s the right thing to do, so... It was an incredibly strategic race for us.
"The start was pretty good so thanks to the team there -- good for us to get away."
Smart strategy
Webber's and second-placed Vettel''s finishes stretched Red Bull's lead at the top of the constructors' standings which they now lead with 383 points, ahead of McLaren on 359.
Vettel also employed smart strategy, holding back from race winner Alonso to prevent his Red Bull from overheating but managing the gap to allow himself a chance right until the very end.
"It was more clever to back off a bit and control the gap because otherwise it can get too hot for the car to stay too close," Vettel said.
"Towards the end that was the story of the race: trying to push him as hard as I could. I think the pace was very good. I think we can be very proud of what we did."
Vettel said the Red Bulls would be competitive in the remaining four races of the season.
"(They) should suit our car very well. The most important thing is the consistency and we have a very strong car and a good team."
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