The coach, whose future after the tournament had been unclear, said he had agreed with Polish FA chief Grzegorz Lato that his contract would not be renewed.
Polish press have speculated for some time that Smuda would be replaced barring a strong showing for the national team at the finals, but creditable performances against Russia and Greece had strengthened the case for him to stay on.
"I don't have to resign because I had a contract until the end of Euro 2012 and I do not see any reason [to quit]; the contract is finishing, because I had come to terms with the head of the FA and I know what will now happen," he told reporters.
"At any rate my adventure with the national team is over," he added.
The Poles, who had fought bravely in a 1-1 draw with Russia on Tuesday, never showed the same application in a game played in very wet conditions.
"We did what we could do. I don't know how to explain the fact that in one game the boys played like they were fired up while in the second game they didn't," Smuda told reporters.
Poland were hampered by the fact that they had automatically qualified for the tournament as co-hosts and did not get the chance to improve their performances in competitive matches.
Smuda said his team showed too much confidence, had not taken their chances in the first half and had paid the price.
"We have to swallow this bitter pill today. We were too sure about the possibility of winning against the Czechs," he said.
"We wanted to counter attack but the Czechs were very solid in defence ... they were pressing and they were better."
Smuda said the players had made progress and expressed confidence the team could qualify for the 2014 World Cup.
In hindsight, their failure to reach the quarter-finals was perhaps sealed in the first game when they allowed 10-man Greece to equalise and escape with a 1-1 draw.
"All in all, we had great moments during this tournament and all we can say is 'Thanks'," said captain Jakub Blaszczykowski, scorer of a thunderous goal against the Russians.
"This is the kind of a moment when one needs to say we need to move on, rethink everything, but such experience is essential," he told reporters.
Poland finished bottom with two points behind Group A winners the Czech Republic, Greece and Russia. Co-hosts Ukraine play England in their final match on Tuesday.
