Jenson Button dedicated the first Indian Grand Prix to the lives of Dan Wheldon and Marco Simoncelli.
and were both killed in accidents this month.
Button - who finished second behind Sebastian Vettel - said: "We've had two fatalities and it's very difficult.
"I knew Dan from a young age so I think we should dedicate this first Indian race to Dan and to Marco, who was the most amazing man to watch on a bike."
The inaugural race at the Buddh International Circuit was preceded by a minute's silence, and Button was joined by Vettel and Ferrari's Fernando Alonso - who finished third - in dedicating the race to the pair.
"It's been a tough weekend for everyone in motorsport," added Button, who raced against Wheldon as a child.
Vettel admitted he had "mixed emotions" after his 11th win of the season, which saw him lead from the front to record another dominant win for Red Bull.
"For everyone who is a fan of motorsports it's been a hard time we had to go through," he said.
"On one hand I'm very happy and proud, but on the other hand you have to pay a certain respect to those two guys who lost their lives.
"I didn't know Dan Wheldon, but I got to know Marco Simoncelli this year and our thoughts are with them. Yes, we take great risks when we jump in the car and we hope nothing happens but you are reminded of these things."
Alonso added: "As Seb and Jenson said, we have mixed feelings. These are sad weeks for motorsport.
"We all raced for them today. We will always remember these two fantastic people."