The Oranje needed a point to progress to the last four ahead of world champions France, but they looked down and out after Timo Werner and Leroy Sane netted for Joachim Low's men.
But Quincy Promes and makeshift centre-forward Virgil van Dijk drew Netherlands level, leaving Koeman delighted despite an underwhelming performance.
"The team showed character. We kept going," Koeman said in quotes published on UEFA.com. "I didn't think we played well.
"Maybe at this stage it's too much for us to play two matches in such a short period of time against such high-quality opposition. Let's not forget, this Germany is an excellent team, maybe even better than France.
"But we also showed that we can recover when playing opponents of this calibre."
UEFA Nations League (@UEFAEURO) November 19, 2018
And Koeman credited his assistants with the masterstroke that was moving defender Van Dijk up front ahead of the captain's decisive equaliser.
"I got that note from Dwight Lodeweges and Kees van Wonderen," he said. "When we were 2-0 down, they asked me if we should change things around and I said, 'Yes'. Next thing I knew I had the note.
"So I gave it to Kenny [Tete] and, in the end, it's fantastic that the equaliser came from the guy who was told on the note to push up front."