Morten Olsen quit as coach of Denmark after 15 years in the hotseat following Tuesday's failure to qualify for Euro 2016.
Denmark drew 2-2 at home to a Zlatan Ibrahimovic-inspired Sweden in Copenhagen to crash out of the Euro play-offs 4-3 on aggregate.
"I've told the players that the Federation and I have agreed that it would make no sense for me to continue," said the 66-year-old Olsen.
"The last few months have been frustrating. I couldn't find consistency either in our performances or our line-up. I take full responsibility."
Olsen took Denmark to the World Cup last 16 in 2002 and the Euro quarter-finals two years later but this was the second tournament in a row for which Denmark had failed to qualify.