Marco Devic thought he had equalised for the co-hosts to bring them potentially within a goal of qualifying for the quarter-finals but Hungarian officials waved play on after a magnificent clearance from England defender John Terry.
Television replays suggested the ball had crossed the line and Ukraine head coach Oleg Blokhin and his team were left fuming while England conceded they had been fortunate.
Goal-line technology is expected to be formally sanctioned by the International Football Association Board (IFAB), who govern the laws of the game, on July 5.
Blatter used Twitter to make clear he supported that move.
"After last night's match, GLT (goal line technology) is no longer an alternative but a necessity," wrote the FIFA president.
FIFA has been trialling two different systems to help officials know whether a ball has crossed the line.
England's friendly against Belgium last month was one of the test matches for Hawk-Eye, the system used in tennis and cricket, although it was not at the disposal of match officials.
A similar system called GoalRef has also been trialled in two Danish league matches.