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."
A FIFA spokesman said the three centimetre ruling applied during initial testing of potential goal-line technology systems last year, but that the two systems ultimately approved by FIFA met much stricter criteria.
The International Football Association Board (IFAB) approved the use of goal-line technology in June and it was used for the first time at the Club World Cup in Japan this month although was not called into action.
The two systems approved are Hawk-Eye, which is used in tennis and cricket and is based on optical recognition with cameras, and GoalRef, which uses a magnetic field with a special ball to identify a goal situation.
Fandel added that Germany was unlikely to use full-time referees and called for automatic red cards for elbowing incidents.
"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."
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