Koubek blamed "stupid mistakes" and exhaustion from heavy travel for his team's World Cup exit after a 3-0 defeat by co-hosts Mexico in their last match left them bottom of Group A with only one point gained in a draw with South Africa.
"A media campaign based on a number of half-truths and fabrications against me also contributed to my decision," Koubek said in a statement.
"In this atmosphere, my work for the Czech national team would no longer make sense."
Koubek took over the national team following a shock qualifying loss to the Faroe Islands and guided the Czechs through the playoffs to reach the World Cup for the first time since 2006.
The players who featured in the successful playoff wins against Ireland and Denmark make up the core of the squad, including Wolverhampton defender Ladislav Krejci and Olympique Lyonnais midfielder Pavel Sulc.
The veteran coach, however, came under intense scrutiny for his defensive approach and a decision to leave star striker Patrik Schick on the bench for a critical clash with Mexico that ended in a 3-0 loss.
