An unfortunate own goal from Timm Klose was the difference at Carrow Road, despite City dominating possession and enjoying much the better chances.
Speaking post-match, Zimmermann said City's dominance and desire could not be questioned in their defeat.
"If you see the reaction of the supporters after the game, that tells you a lot about how we played today," he said.
"It's been an unlucky loss. They might have had one shot on target in the first-half and still they won the game.
"We've tried our best and I can't blame anybody. I can't complain that somebody didn't give their best.
"That's why you're very disappointed with the result, especially when you have the international break for the next two weeks.
"But as I said, I can't blame anybody because the commitment was okay today. It's just very unfortunate with the result."