The Oranje needed a point to progress to the last four ahead of world champion France, but it looked down and out after Timo Werner and Leroy Sane netted for Joachim Low's men, FourFourTwo reported.
But Quincy Promes and makeshift center-forward Virgil van Dijk drew the Netherlands level, leaving Koeman delighted despite an underwhelming performance.
"The team showed character. We kept going," Koeman said.
"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 caliber."
And Koeman credited his assistants with the masterstroke that was moving defender Van Dijk up front ahead of the captain's decisive equalizer.
"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 equalizer came from the guy who was told on the note to push up front."
Van Dijk was proud of the Netherlands' incredible efforts, but he said their focus is on qualifying for Euro 2020.
After the Netherlands' failure to reach Euro 2016 and World Cup 2018, Van Dijk's main concern is getting to the next major international tournament, looking beyond the conclusion of the Nations League.
"It's a fantastic feeling. We should all be proud of ourselves. I know I am," Van Dijk said, according to uefa.com. "It's just a great feeling for all of us.
"We worked so hard every game and to get rewards for that is fantastic.
"Hopefully [the future] holds a lot, but we don't like to look too far ahead. We want to qualify for Euro 2020, that's the main target.
"If we can win the Nations League, fantastic, but we all want to make sure we're at the European Championships and do very well there to make our country proud."
Van Dijk explained why he consoled the referee after the match.
Once the full-time whistle sounded at the Veltins Arena, Van Dijk consoled Romanian referee Ovidiu Hategan.
Van Dijk revealed the reason for the beautiful gesture was because the official had learned of his mother's passing, with Digi Sport reporting that Hategan heard the news at half-time of the match after asking his family to be kept informed.
In quotes reported by Voetbal International, he said, "He told me his mum recently passed away. He broke down and started crying.
"I consoled him and told him he refereed well.
"It's a small thing, but I hope it helped."