The Scots twice levelled against the world champions and went in all square at the break, but they couldn't respond to Ilkay Gundogan's 54th-minute winner.
Strachan told BBC Sport: "There's a couple of times in my managerial career where I get angry or sad. Actually, at this point, you feel for the players.
"Whatever you think, over two games they've put in some amount of work. Sometimes football is more than what you drink, what you eat and how you train. It's inside you. No-one can tell me that every one of those guys has something inside them that drives them on.
"To stand up, after going behind to the world champions [twice] and to keep coming back, keep plugging away - they can be proud of their performances."
Scotland sit fourth in Group D following the defeat, four points behind the Republic of Ireland.