"After last night's match, GLT (goal line technology) is no longer an alternative but a necessity," the president of football's world governing body Sepp Blatter wrote on the micro-blogging site Twitter.
Ukraine striker Marko Devic came close to equalise for the co-hosts to bring them closer to qualifying for the quarter-finals but Hungarian referee Viktor Kassai waved play on after the clearance from England defender John Terry.
Television replays showed the ball had clearly crossed the line and Ukraine coach Oleg Blokhin and his players were left fuming.
Similar case went in Italy striker Antonio Cassano's favour when a sharp-eyed fifth official correctly called that his header had crossed the line in the 2-0 win against Ireland.
FIFA is currently trialling two types of goal-line technology, one from British firm HawkEye, which uses a series of cameras in stadium roofs to track the trajectory of the ball and another from German firm GoalRef, which uses sensors.
Both have been tested in match conditions in recent months, with monitors observing the performance of HawkEye during England's pre-Euro 2012 warm-up game against Belgium at Wembley stadium.