The Greeks said they alerted Romanian officials before the game in Athens after they named only two goalkeepers because first choice Ciprian Tatarusanu was injured and not included in the squad list.
Under FIFA rules, any 23-man squad for an official game must include three goalkeepers. The oversight was missed by FIFA officials at the time.
Greece won the game 3-1 at the Karaiskakis Stadium and clinched their place in the finals after drawing 1-1 in the second leg on Tuesday.
"With so much at stake - participation in a World Cup and the financial gains for the Greek FA which comes with that -- we could have ignored their error and taken the result, but it was important to do the right thing," Fysass told Greek radio SportFM.
"I preferred to qualify on the pitch rather than on paper."
Bogdan Lobont started in goal with Costel Pantilimon on the bench in the first leg last Friday with the Romanians adding an outfield player as the third keeper to keep within the rules.
Romanian FA spokesman Paul Zaharia declined to comment on the claims made by Greece but told Reuters by email: "The Romanian match sheet has been done according to the Laws of the Game and to the competition's regulations.
"A goalkeeper can be fielded as an outfield player and so an outfield player can be fielded as a goalkeeper, if the coach decided like this.
"Our match sheet had 23 players, three of them being goalkeepers and one of those three was an outfield player, so that everything was done due to all the rules and regulations."
Fysass's faith in his Greece team was justified with two goals from Konstantinos Mitroglou and one from Dimitrios Salpingidis helping them to victory in Athens. A draw in Bucharest saw Greece reach next year's finals 4-2 on aggregate.
Tatarusanu returned for the second leg with Lobont and Pantilimon named among the substitutes.
- Sports & Recreation