Per Mertesacker scored the game's only goal on 39 minutes to see the visitors to victory as both teams continue preparations for the 2014 FIFA World Cup.
Low said his team should have wrapped up the result with a second goal but was nonetheless pleased with his side.
"Over the 90 minutes we deserved to win this game. We had a good grip on the game," he said.
"What we missed was converting a few chances on the break, especially in the second half, to seal the game earlier than we did.
"I was annoyed at times because we really squandered our chances, many of them when we should have extended our lead much earlier – especially when England were open in defence, we should have scored that second goal."
Low described Arsenal defender Mertesacker as a 'pillar of strength', but was full of praise for his whole team.
Manuel Neuer, Philipp Lahm and Thomas Muller were among several squad members to play no part after featuring in Germany's 1-1 draw against Italy on Friday.
"I can approach 2014 with a sense of quiet confidence," Low said.
"Many of the players who I wanted to test here today can be proud to have withstood the pressure of playing against such a great crowd."
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