Herbert Fandel cited a regulation which he said permitted a three-centimetre margin of error for technology used to decide whether the ball has crossed the goal-line.
He also referred to Ukraine's goal against England at Euro 2012 which was disallowed after officials failed to spot that the ball had crossed the line.
"There are doubts as to see whether the goal-line works 100 percent," Fandel told the DFB's website on Monday.
"A margin of error of three centimeters is understandably still a bit too high, especially when you consider that the ball in England's Euro 2012 match against Ukraine was only a few centimetres behind the line."
"That would mean that the system would possibly not have recognised that goal. If you spend a lot of money for something, then it must be working properly."
"In our view, a professional referee, who has no profession apart from football, is not likely in the future," he said.
"I would like a tougher line [for elbowing]. I find it very hard to accept that a player who hits an opponent in the face or ruthlessly elbows him is not sent from the field with a red card.
"Players who punch and stamp do not belong on a football field."
