"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.
"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."
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
"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.
"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."
