A mourning Michael Schumacher said he did what his mother would have wanted him to do after winning Sunday's San Marino Formula One Grand Prix hours after her death.

"My mother loved to be at the karting track when we were in our karts in Kerpen and loved to see us racing," Schumacher's spokeswoman Sabine Kehm quoted Ferrari's five-times world champion as saying.

"My mother and father had always supported us. They made it possible to do what we do and she would have wanted that we did this race today, I am sure."

Elisabeth Schumacher, 55, died in hospital in Cologne on Sunday morning after both Michael and his younger brother Ralf paid a final visit on Saturday after qualifying first and second on the grid. She had been in a coma for some time.

"Everybody in the team -- our president, technicians, mechanics, the cook -- has given me the feeling, over this terrible day today, how much they back me," said Schumacher. "It did me good."

Schumacher appeared on the podium wearing a black armband after the race and did not open the winner's traditional champagne after a win that would normally have had the Ferrari faithful spilling out onto the track in delight.

He was excused from the later news conference.

Team boss Jean Todt joined in praise for the driver.

"It was very difficult for him today and he did the job because he felt he wanted to," he said. "He did fantastic work for the team. On top of that, he's a driver.

"I think it's important that he shows what a man he is and that's maybe the most important thing today."

British rival David Coulthard, who finished fifth for McLaren, added his condolences.

"You try and imagine yourself in that situation and all you can say is that you imagine your mother or father would want you to do it because they've supported you from such an early stage," he said.

"But it must have been on their mind, a really uncomfortable position for them to be in. But I admire the fact that they got on and did the job."

Coulthard recalled his own situation after surviving a plane crash in 1999 that killed both his pilots.

He said he had "just a few hours of what do I want to with my life scenario but it was purely personal rather than involving some other member of the family. So it's not anywhere near close to what they are having to go through."