At one stage his men were one goal away from elimination.
With Portugal leading against Holland going into the last 20 minutes, one goal for Denmark would have been enough to see them qualify together with the Portuguese and send Germany, who had won their first two group games, back home.
But Lars Bender's goal handed Germany a 2-1 victory and ended any doubt.
"I had a plan," said Low. "Of course I had considered what would have happened if Denmark had in some way suddenly scored a goal but I never had that feeling.
"I was pretty relaxed because it doesn't get you anywhere when you panic.
"Bastian Schweinsteiger and Sami Khedira were always in control and I just had the feeling we would score."
Low's confidence was based on what he had seen in the first hour of the game in Lviv, during which Germany appeared in control.
"Denmark played with a stoic calmness and it seemed like they could not care less," he said.
"I never had the feeling that Denmark were playing to win it. They wanted to keep the result, were happy with the draw and then maybe they would get a free-kick or corner that they could take advantage of, but they did not attack much.
"They sat back a lot, even though they had to win. They had one or two good chances, but no more than that, and I think in the second half we did a decent job given the pressure.
"Maybe had we played Holland or Portugal (in the final group game), they would have done more for a win than Denmark did."
Nevertheless, Low was not fully satisfied with his own side's performance and said they can get better, despite coming through the group with a 100% record. They play Greece in the quarter-finals.
"We missed three or four chances and did not have the killer instinct," he said.
"I think that in midfield and at the back, there were often plenty of gaps and we could have got control of Denmark better.
"Greece will be similar and will try to take the tempo out like Denmark. We can still improve."
Denmark coach Morten Olsen expressed his pride at his side's performance and explained why Low had the impression that his side was so negative.
"If you try to put them under pressure, then you can get punished quickly," he said.
"One-one was a good result for us because then you just need a lucky punch maybe with a set-piece, but if you gamble too much, they can hit you quickly.
"We are disappointed not to have gone through, but this team has a future.
"Compliments to all of our players - they played a great tournament and it is only minor details which make a difference."
One of those minor details was a penalty appeal when Nicklas Bendtner had his shirt tugged by Holger Badstuber inside the Germany penalty area, impeding him from doing more with a one-on-one situation with Germany goalkeeper Manuel Neuer.
That incident happened just minutes before Bender netted Germany's winner and it was a moment which could have decided the encounter and indeed the group in Denmark's favour.
"I think we should have had a penalty," said Olsen. "It is not permitted to pull your opponent's shirt in the box and that is what this extra referee is there for, but clearly he did not see it."
Olsen was not making that his principle excuse for defeat and elimination, however.
"Maybe we lost it by not holding Portugal to a draw, but there are so many ifs and buts," he said.
"When all is said and done, we have done very well at this tournament."