Vettel paid tribute to MotoGP rider Marco Simoncelli and IndyCar racer Dan Wheldon, who succumbed to fatal crashes recently while racing in different circuits.
Indian Grand Prix - a job well done
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"We pray that every time nothing happens as Marco Simoncelli and Dan Wheldon disappeared last week-end and we will never forget these young commited two drivers," he said.
The Red Bull driver said his team is still hungry to win and he is looking forward to races at Abu Dhabi and Brazil.
"The car is fantastic. The team is enjoying the performance. When I walk in the garage, I see that the guys are working very hard. We are still hungry. It is a fantastic achievement. I am looking at the two next races," said Vettel, who will next bid to equal Michael Schumacher's 13 F1 win record in a season.
The 24-year-old said the circuit was challenging and a good start was very important.
"It is very challenging. It is very easy to go over the limit and to end up in the dust. Then you have to fight your way back. It is not so easy with traffic," he said.
"The start was important. I was focusing a lot on turn 3. It was crucial to have a clean exit. I was able to pull away in the first laps. Jenson pitted. We had to react. The second sting was more tricky to manage.
"The tires were a bit of an issue. But I found the rhythm again. After Jenson pitted, we reacted the lap after. Then I was able to push. We wanted to have Jenson in the mirrors and that is where we kept him," he added.
Vettel said a new track poses many questions but now that they have the experience of racing, they would have more data for next year.Vettel wins inaugural Indian GP, Sutil ninth
"It is always clear than when there is a new track there are many questions to answer. Like tire choice. We knew about the soft tires. We were not sure if we had to pit twice or three times. These days we get an idea about the track. It is different when it is new," he said.
"We have more data for next year and we can understand more for the car and for the setup. It is more difficult for strategy, set-up when the track is new. As of now, our life will be a lot easier."
McLaren Mercedes driver Jenson Button, who finished second at the podium, said it was a fantastic race and dedicated it to Marco and Dan.
"I am fantastically happy. I got a good start and then I was trying to match Sebastian's pace. Yesterday I had a disaster in qualifying but it was a good race," he said.
"It was a tough week-end last week with two fatalities. I knew Dan very well. It is a very sad race. I think we should dedicate this race to Marco and Dan."
The 31-year-old British said he lacked pace to catch up with Vettel but overall it was a good race.More on Sports
"I had Mark behind me. I was able to pull away. It was a fun race. We did a good job. The pace is not quite there. But we will make up," he said.
"The race was very different. I had a good start and then it was about judging where to put the car on turn 3. You have to be very careful where to put the car on turn 3. Mark pushed me very hard. We had a go on turn 4. In the end it was tricky.
"The guys on the team did a tremendous pit-stop. The pace was good. But when Sebastian was in the rhythm, we could not touche him. We did not have the pace.
"I hope that Sebastian is not untouchable. He is difficult to challenge. We tried everything today. But Sebastian and Red Bull were untouchable. We hope we can challenge him," he added.
Button also congratulated his team and said they will push hard for a strong finish in the next two races.
"I want to congratulate the team for winning the second place for constructor. This means we are strong for the next two races. I am very excited with the challenge from Abu Dhabi and Brazil," he said.
Ferrari driver Fernando Alonso too was pleased to finish third but rued their complicated start at the Budd International circuit on Sunday.
"I am very pleased with this podium. It is fantastic to be on the podium on occasion of a first ever Grand Prix. As for us at Ferrari, we did not make the perfect start. We lost a few positions," he said.
"The second pit-stop was a bit complicated as we did two extra laps. The hard tires were not as good as the stops. The team did the right call. We were calm and we tried to take the advantage from the extra two laps.
"In the last stint it was a bit of a question mark. Even if we were third at that point of the race, we were not sure how it would go. If more laps, the podium would have been more difficult," he reckoned.
Talking about the recent deaths of Marco and Dan, the 30-year-old Spanish said, "Mixed Feelings after sad days for motor-sports with two fatalities and we will remember these two fantastic friends."
Alonso also had good things to say about the circuit. "The circuit was fantastic for 60 laps. It is very nice to drive. It was a narrow line from normal line. It will improve. The circuit has a bit of everything: Hairpin, good start," he said.
"Two DRS zone which worked ok with more overtaking possibilities and a good combination of corners in 5th and 6th gear which we love to drive.
"The circuit itself will improve too. There was too much sand the first day. Now the circuit is in a very good conditions. There were a bit of issued on the kerb with my team-mate, there will be a better solution on this subject to avoid any risk or any accident," he added.
Although two more races are still to go, both drivers and constructor champions have been decided and Alonso said his priority would be to focus on 2012.
"Two races left and 13 points away from Jenson. There are 50 points still available in the last two races of the season. Finishing second is better than fifth. But it is not a big priority for us to get a better position in the championship.
"This season, I will remember my win in Silverstone or a few great podiums. But once the championship is not in our hand, what can we do? The team worked well on my car. My priority will be 2012," he signed off.