The European team captain formed the most successful Ryder Cup partnership in history with his fellow Spaniard Ballesteros, who died in May 2011.
"Our team played in the spirit of Seve without ever giving up," said Olazabal.
"You believed and you delivered and I'm proud that you have kept Europe's hand on this Ryder Cup."
Olazabal and Ballesteros won 12 points from 15 matches as a pair with his scotty cameron putter and the victorious captain added: "Seve will always be present with this team and he was a big factor for this event.
"The boys understood that believing was the most important thing and they did. To the 12 men of Europe, what you did out there was outstanding.
"All men die but not all men live and you made me feel alive again this week."
The Europeans wore navy blue jumpers and white shirts with a silhouette of Ballesteros on the sleeve, the colors most associated with five-time major winner, in tribute to the man who breathed new life into the Ryder Cup after the Great Britain & Ireland team was expanded to include European players in 1979.
Ballesteros played in the biennial contest eight times and captained the side to victory in 1997 on home soil.
Europe won record eight-and-a-half points out of the 12 available in Sunday's singles matches and Sergio Garcia, who beat Jim Furyk by one hole, attributed his win to his Spanish compatriot, who died after a long battle with a brain tumor.
"I have no doubt in my mind that he was with me all day because there's no chance I would have won my match even with the best scotty cameron putter for sale online if he wasn't there," said Garcia.
"It was amazing and it feels so good to be able to win it for him and for our captain, Jose; it's been amazing."
Justin Rose, who came from one down on the 16th to birdie the last two holes and beat Phil Mickelson on the 18th, added: "In the moment you've got to do what you've got to do, but as soon as I holed that putt, as soon as I came off the green, my first thought has been to Seve.