"Our boys were rewarded today for an unbelievable passion and fighting spirit. We said that no road should be too far and before you have success you have to have the gods sweating for you," he told reporters.
Greece, who had come as underdogs following their 0-0 draw in the first leg of the European play-off in Athens four days ago, stunned the hosts with a first-half goal from Dimitris Salpigidis.
The German coach was under mounting pressure following Greece's second-place group finish after losing both matches against Switzerland to miss out on automatic qualification for the finals in South Africa.
Despite stinging media criticism following their lacklustre performance in the first leg where Greece fielded five defenders, he stuck to his guns and again flooded his back line.
"We will play exciting football when we have (Lionel) Messi, Kaka, (Andres) Iniesta and Xavi on the team," Rehhagel said jokingly.
"The Ukrainians had very good combinations but we knew we would play with counter-attacks anyway and one was a success."
Rehhagel, who took charge of Greece in 2001, has now steered the 2004 European champions to one World Cup and two European championships in his eight years at the helm.
The World Cup will also be the final missing piece of the puzzle for Rehhagel's 50-year plus career in the game. The 71-year-old has never competed in it, neither as a player nor as a coach.
PAINFUL EXIT
Ukraine, hoping to make it to their second consecutive World Cup, had their opponents on the back foot for much of the game but failed to score.
"It is very painful to end the campaign like this because we deserved to be at the World Cup. We lacked a bit of maturity to fulfil our dream," coach Olexiy Mikhailichenko told reporters.
He said a ticket row over prices had left far too many empty seats in the 50,000-seater stadium.
"This ticket row did not help us for sure. Some personal ambitions did not allow us to have a full house. I had the feeling we were playing on a neutral pitch."
