The twist recalls the memory of England's highly controversial goal in the 1966 World Cup final against Germany, which was awarded and helped England lift the trophy with a 4-2 win on home soil.
Ever since then, Germany have had the hex over the Three Lions at the World Cup, winning in 1970, drawing in 1982 and triumphing in the penalty shoot out in 1990.
L?w admitted the referee's mistake but emphasized their domination in most of the time.
"From TV images, I have to say this ball was across the line. It should be awarded," L?w said.
"After 2-0, we took control of the game. I have to say we were dominant over long patches.
"We were very aggressive, very pushy from the first minute. Our midfielders were very creative and helped us penetrate their defence. We should have been three to nil in the first half," he added.
Klose bagged his 50th goal for Germany and his personal 12th in the World Cup, only three short of Brazilian Ronaldo's record 15. The Bayern Munich forward could have even added two more but saw his efforts blocked.
Opposite to the tension before the game, both sides started lack of creativity and inspiration until when a Germany's long cross found dashing Miroslav Klose well, who held off Matt Upson in the box to poke the ball past David James.
At 2-1 down in the second half, Lampard had another chance to level the score but his free-kick hit the bar, again, and went wide this time.
The final stage of the match was all about Germans' break with pace and Mueller's brace were the fine conclusions of two lightening counter-attacks.
In the 67th minute, Bastian Schweinsteiger played a perfect pass for Mueller, who inside the area, smashed it off the body of David James and into the net. The 20-year-old grabbed his third goal in the tournament three minutes later when he whacked in Mesut Oezil's pass along the six-yard box.
In Monday's World Cup action, the Netherlands face Slovakia and Brazil take on Chile.