"I won't put myself above the team. That would be wrong," Hogmo told a news conference five days after losing 2-1 to the Czech Republic in Prague.
Norway failed to qualify for the 2014 World Cup and the Euro 2016 tournaments, and currently sits fifth out of six teams in the ongoing race to reach the 2018 World Cup in Russia.
The team's ranking by FIFA, the international soccer federation, recently plunged to an all-time low 81st in the world, down from 24th in 2012.
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Hogmo and NFF had mutually agreed to his resignation, the federation said.
(Reporting by Ole Petter Skonnord, writing by Terje Solsvik; editing by Amlan Chakraborty)
