The closest Roy Hodgson's team came to an equalizer was when Andros Townsend struck the post from a long-range strike on a night when Germany goalkeeper Roman Weidenfeller had little to do.
Germany fans celebrated the win by singing in English "Football's coming home" taken from the England anthem "Three Lions."
It was a miserable way for the English Football Association to round out its 150th anniversary celebrations in front of a 85,934-strong crowd, with Germany exposing the hosts' technical deficiencies.
"It was a harsh defeat but we needed better quality," Hodgson said. "The effort, the work rate and desire, I can't fault at all. But in the time we had the ball in the German half, we weren't as efficient as the Germans were when they had the ball in our half.
"The quality of our passing and shooting was not as good as the Germans."
England, which beat Germany here in the 1966 World Cup final, was only spared a heavier defeat against a fellow Brazil 2014 qualifier by Joe Hart's saves.
The Manchester City goalkeeper, who was rested in the Chile friendly, provided a reminder of his abilities three weeks after being dropped by his club following a series of blunders.
A minute before Mertesacker scored his fourth international goal, Hart pulled off a one-handed save to thwart another header from the defender.
"We knew set-pieces would be a danger, they had some big players and we were a small team tonight," Hodgson said.
Hart wasn't at fault for the goal, with England too porous as Mertesacker evaded Wayne Rooney and Chris Smalling to head home.
"Per definitely organized our defense he has turned out to be a pillar of strength literally speaking in terms of his height," Loew said, praising Mertesacker's agility and ball distribution.
He helped to ensure England was largely restricted to striking from distance, with captain Steven Gerrard sending the ball onto the roof of the net just before half time.
Four minutes into the second half, a fine save from Hart kept out Marco Reus' fierce strike after Mario Gotze skipped through the home defense with ease.
Mertesacker was left in space again to try again with his head, but nodded over from a corner, while a low save from Hart pushed away Gotze's effort.
"I was annoyed at times because we really squandered our chances many of them when we should have extended our lead much earlier," Loew said. "Especially when England were open in defense, we should have scored that second goal."
There were eight changes from the Germany lineup which drew with Italy on Friday as Loew took the friendly as the last chance to experiment, with big names including Bastian Schweinsteiger, Mesut Ozil and captain Philipp Lahm absent.
But the international year ahead of the World Cup ended for Germany just as it had begun against France with an away win.
"I can approach 2014 with a sense of quiet confidence," Loew 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."
