Die Nationalmannschaft progressed to the quarter-finals following a tight encounter on Monday night, with extra-time strikes from Andre Schurrle and Mesut Ozil giving them a two-goal before Abdelmoumene Djabou pulled one back late on.
Neuer's performance in the game in Porto Alegre was defined by the number of occasions that he rushed from his box to help his defence and, whilst backing the Bayern Munich shot stopper, Beckenbauer acknowledged he was taking some significant risks.
"I would not say he's a better sweeper [than me]," the 68-year-old told a press conference.
"But he's a better sweeper in terms of sweeping away the opponent. Yes, Manuel Neuer saved us in some situations, such as an outfield player would do. But he threw caution to the wind.
"Twice he was lucky that he met the ball at exactly the right time for the attack. If he would have come in too late, he could have been sent off. With all due praise for his great performance
"I would prefer that he remains in goal against France. If Mats Hummels is fit again, the defence is also more stable."
Der Kaiser, who was a World Cup winner as a player in 1974 and also led West Germany to victory in 1990 as head coach, also dismissed criticism of Joachim Low's tactics, especially with regards to his decision to play Philipp Lahm in midfield."We should be glad that we have such a flexible player like Philipp Lahm," he continued.
"There is no one like him out there. He fully convinced me against Algeria in the midfield. One thing is clear though; without Lahm at the back there is more pressure on the right wing.
"Jogi Low should not be talking to others outside the camp. I have never read a DFB team manager during a World Cup listening to a newspaper or taking tips from outside. "
Germany now face France in the quarter-finals in Rio on Friday and Beckenbauer is adamant that they will not underestimate their opponents as they may have done with Algeria and the United States.
"France are our strongest World Cup opponents [so far]," the German added.
"Coach Didier Deschamps has turned a fractious bunch into a confident force. Even though it sounds paradoxical, against the French we will play more easily.
"Subconsciously, we have underestimated the United States and Algeria. That will not happen against the French."