Frings was omitted from Germany's starting line-up in their thrilling 3-2 Euro 2008 semi-final success over surprise package Turkey on Wednesday.
However, despite the disappointment of not starting, Frings responded by admitting to Low that he would not have started himself had he been at the helm.
"He was very disappointed when I told him but later he came and knocked on my door and said he would have made exactly the same decision if he'd been the coach," said Low.
"It showed just how big a player he is - what a leader he is. It was a classy reaction."