Israel finished fourth in Group B behind the Belgians and Group B runners-up Wales, who will both play at the finals, and third-placed Bosnia, who took the playoff spot.
"Ultimately, we are all measured by results. I set myself a target to finish in third place (in the group). We did not achieve this aim and I am stepping aside," Guttman said at Tel Aviv airport as the team returned from Belgium.
Their bid to reach the finals in France began with three straight wins but was followed by losses at home to Wales, Cyprus and Belgium, a sequence that highlighted Guttman's inability to build consistency.
"I have not been able to leave my mark on the team," he said after Cyprus won 2-1 in Jerusalem on Saturday. Israel's only haul of maximum points came against group minnows Andorra.
Guttman's appointment in 2011 was widely welcomed but his charges disappointed with dour displays in the 2014 World Cup qualifiers, when they finished third in a group that included Russia, Portugal, Azerbaijan, Northern Ireland and Luxembourg.
In a coaching career of over 30 years, Guttman, 57, has managed several clubs. He had most success at Hapoel Haifa and Hapoel Tel Aviv, winning two league titles and three State Cups. He also coached Cypriot sides Paralimni and AEL Limassol.
Media reports in Israel say mid-table Hapoel Tel Aviv are interested in re-hiring him as they seek to regain their once-dominant position in Israeli soccer.
(Writing by Ori Lewis; Editing by Neville Dalton)
