The centre-back netted in the closing minutes to complete a comeback for Ronald Koeman's side and send them into the semi-finals of the tournament. Germany had been 2-0 up at half-time, but the draw saw them relegated from the group with just two points while sealing the team's worst run in 40 years.
Although Bayern Munich star Muller was happy with his side's display overall, the late disappointment was a typical way to end a year that included their group stage elimination from the World Cup.
"It’s a strange feeling, as it was a positive performance – which we have been waiting a while for," he told the DFB's official website. "We used the momentum from the last two games and there were many positives to take from the game. We defended well for 82 minutes and put together some good attacks.
"One thing I would say is that we should have made it 3-0 and sealed the win. Suddenly it was 2-2 and the referee has blown for full time – it was like a horror film. The team didn’t deserve to not win the game, but this result is typical of our year in general.
"Ultimately we want to take the positives into our next few games. I’m certain that we are going in the right direction.
"None of us can see into the future, but it is clear that the side is having more playing together and feels more united. We enjoy each other’s successes and want to work together to improve certain things. We know that we are making progress still. But I am sad that we are here talking about draw and not a convincing 3-0 win."
He added: "If you take the whole year into account, it was statistically our worst year. However, we have recently gained some new momentum, which we can look to build upon next year. We may not be back among the world’s best teams, but we have shown that we can play some good football – even with a different side."
The 29-year-old attacker made his 100th appearance when he came on midway through the second half, but he decided not to celebrate the occasion with a beer.
"I don’t think now is the right time to have one," he said. "It’s hard to get over the fact that we only drew the game. Obviously my teammates and the coach congratulated me, but I turn up for international duty to win games and experience wins. It’s naturally a big personal achievement, but I didn’t wake up to get my 100th, I woke up to beat the Netherlands."