McClaren, who took over as Jamaica boss in July last year, announced his decision shortly after his team were held to a 0-0 draw by Curacao in their final qualifier.
Jamaica needed to win the game at Kingston's National Stadium to qualify for the World Cup, but instead could only watch as tiny Curacao held on to advance to the tournament instead.
It was another bitter qualification flop for McClaren, who also famously failed to take a star-studded England team to the 2008 European Championship.
"I have given everything I have to this job, to this role," McClaren said in a statement at the start of Tuesday's post-game press conference.
"Leading this team really has been one of the greatest honours of my career. But football is a results business and tonight we've fallen short of our goal, which was to qualify from this group.
"It is the responsibility of the leader to step forward, take accountability and make decisions in the best interest of the team, for them to go forward.
"After deep reflection and an honest assessment of where we are and where we need to go, I have decided to step down as the head coach."
The 64-year-old's resignation leaves Jamaica scrambling to find a head coach before next year's Inter-Confederation play-offs, which will include Iraq, Democratic Republic of Congo, New Caledonia, Bolivia and Suriname.