With his team trailing 10-6 overnight, the 46-year-old Spaniard masterminded a thrilling 14 1/2-13 1/2 win over the USA on Sunday.
Olazabal says that belief played a vital role in his side's triumph.
"When I saw that we had a chance this afternoon coming down the stretch I was very emotional," he told BBC Sport. "I started to think of the possibility of winning. My boys have done an unbelievable job.
"I have a few thoughts for my friend Seve [Ballesteros]. This one is for him. This event is so special. Look at 12 men like this, giving their hearts and trying to win the trophy. You don't see this anywhere else in any other tournament. They have given you their best, 120%. They have sacrificed themselves for the benefit of the team.
"I cannot explain today, the guys did a wonderful job. Maybe they knew how much it meant to me. Last night in the meeting I told them that I really believed they could do it. The pairings were well balanced and they just believed in themselves. That's why we are here as winners.
"Those first five matches today were close and key. We managed to win those. This is number one in my list of achievements. More than any of my majors."
Olazabal has won six PGA Tour events during his career. He has also won the Masters Tournament on two occasions.