The European team came from 10-4 down at one point, and 10-6 down going into the singles matches, to clinch a remarkable win at Medinah by 14 1/2 points to 13 1/2.
Olazabal told a press conference at Heathrow: "(Being captain) is difficult, in a way it's torture.
"It's really tough on your nerves, but that's the beauty of the Ryder Cup. It's a huge adrenaline flow and that's what we live for to be honest - the pressure, the tension the adrenaline flow makes us feel alive."
The Spaniard added: "I don't know if it's (the comeback) a miracle, but it's something extraordinary to be honest.
"We haven't seen that before.
"What the players achieved that day was just amazing. It's up to you to decide if it's the greatest moment or the greatest comeback in history but they (the players) deserve all the credit."
Olazabal added: "We have this wonderful trophy here with us because of the huge achievement of those 12 men. They didn't stop believing and the performance they showed on Sunday was just incredible."
The captain has been inundated by messages of congratulation from the likes of Rafael Nadal and also the King of Spain.
"He was, like me, pretty much over the moon," said Olazabal. "That was a nice one."
Olazabal confirmed he would not be looking to take on the captaincy again, saying: "I can assure you that's going to be a no, period."
He claimed there were plenty of other worthy candidates, pointing to the likes of Darren Clarke, Paul McGinley, Thomas Bjorn, Paul Lawrie, Lee Westwood and Padraig Harrington.
"It would be unfair of me to just name one for the next Ryder Cup," he said. "All of them deserve that position."
Olazabal revealed there was one moment on Sunday when he could sense victory was within reach.
"Saturday afternoon was crucial, those last two matches were crucial for the outcome of the cup," he said.
"But it's true on Sunday there was a moment which was quite special. I was standing on the 12th tee waiting for Lee to come on to the tee and I looked at the board and at that point all five matches had already been won by Europe."
He added: "Lee came on to the tee and asked how we were doing. I had done my maths and knew we still had a chance of winning it and I had to walk away, I was very emotional at that point."
The Spaniard was even able to take Rory McIlroy's poor time-keeping in his stride.
Thinking that his match with Keegan Bradley started at 12.25pm instead of 11.25am, McIlroy was still at the team hotel when he got a panicked phone call telling him he had 25 minutes to get to the first tee.
The world number one had read the tee times on his phone in Eastern time, while Medinah operates on Central time, and he was given an escort to the course by a state trooper.
Olazabal added: "Luckily enough a police car was there and he made it on time. It was no surprise at all he managed to win his point."