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.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"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.
Fysass's faith in his team was justified with two goals from Konstantinos Mitroglou and one from Dimitrios Salpingidis helping them to a 3-1 win in Athens. A 1-1 draw in Bucharest in the return saw Greece through to next year's finals 4-2 on aggregate.
Tatarusanu returned for the second leg with both Lobont and Pantilimon named among the substitutes.
(Reporting by Graham Wood; Editing by Mike Collett and Justin Palmer)
