Zutautas leaves Lithuania post
"Since I, as manager, failed to fulfil the task, I am ending my work with the team," Zutautas said.
Zutautas, 39, who replaced Portuguese Jose Couceiro in February 2010, had long been under fire over his side's showing in the race to qualify for next year's tournament in Poland and Ukraine.
Lithuania managed only one victory in eight games - a 1-0 away win against the Czechs in September 2010. Rubbing salt into the wound, they lost 2-0 away to bottom side Liechtenstein last June and then drew September's return match 0-0.
Lithuania's loss also crushed Scotland's hopes for a berth in next month's EURO 2012 play-offs. The result meant the Czechs finished second and took the play-off spot.
Scotland finished third, behind reigning European and world champions Spain, to whom they lost 3-1 last night. Lithuania, who have never qualified for a major tournament, finished fourth ahead of Liechtenstein.