The Liverpool defender chose the perfect stage to net the first brace of his career - bookending the scoring either side of a Karim Benzema effort - as France overturned a 2-0 first-leg deficit to progress 3-2 on aggregate.
The result sparked wild scenes of celebration among a Stade de France crowd so often hostile to the players, and Sakho revelled in the occasion.
"There's pure happiness and we've written a page in French football history with this," the 23-year-old said.
"A lot of people didn't believe in us but there were also plenty who did.
"France showed a lot of virtues and it was extraordinary for everybody."
Asked about his own contribution, he said: "I don't see myself as a hero; the team was the hero in this one. I'd never previously scored a double in my career.
"We're going to Brazil and we have to take on board the lessons from all of our matches, not just this one."
Sakho opened the scoring with a close-range finish in the 22nd minute before two erroneous offside decisions balanced each other out as Benzema scored in the 34th minute - moments after seeing another effort disallowed.
After Ukraine had Yevhen Khacheridi sent off, Sakho popped up again with 18 minutes remaining to bundle the ball home from Franck Ribery's drilled cross.
France coach Didier Deschamps insisted the tie was far from over ahead of the match despite the pessimism of many of his countrymen, and the 1998 World Cup winner was delighted his faith was vindicated.
"It's fabulous, especially after what happened in the first leg as we turned the situation around," he said.
"The players deserve all the credit as they've done something great. It's a source of great satisfaction to the players, the coaching staff and to French football as a whole.
"I'm proud of the players and they can be proud of themselves for having fulfilled the objective.
"I was a player once and I know that it's players who write history."
Midfielder Ribery added: "It's magnificent and extraordinary. The supporters played their part. There had been a lot of sadness in the past and this is great.
"I hadn't seen the Stade de France like that for a long time.
"We suffered a setback in Ukraine but we reacted."
Ukraine coach Mikhail Fomenko admitted his players had cracked under the pressure.
"I've got a lot of regrets," he said. "Our psychological approach wasn't good. We needed to be ready and I don't think we were.
"We made mistakes in defence and didn't play the way I wanted us to."