It was largely expected that Smuda would drop midfielder Tomasz Jodlowiec and striker Michal Kucharczyk, who had fared poorly in a friendly win against Latvia, as well as defender Kamil Glik from his provisional group of 26.
"I would like to thank them because they gave it their best, they worked at full capacity and I hope they stay in contention for squads in the future," Smuda told a news conference.
On Saturday, Poland's number two goalkeeper Lukasz Fabianski was officially ruled out of the tournament after injury his shoulder at Poland's training camp in Austria.
"I never was so frightened as during yesterday's game (against Slovakia). I never felt like that before in my life. I was just thinking please make sure nobody gets injured," Smuda added after his side came through the 1-0 win unscathed.
Poland are due to play their last friendly on June 2 against Andorra.
The European Championship, being co-hosted with Ukraine, kicks off on June 8 when Poland face Greece in the opening match at Warsaw's newly built National Stadium. Czech Republic and Russia are also in Group A.
"All four (in the group) have a chance, but Russia is the favourite. The first match against Greece will set the pace," Smuda said.
Goalkeepers: Wojciech Szczesny (Arsenal), Przemyslaw Tyton (PSV Eindhoven), Grzegorz Sandomierski (Jagiellonia Bialystok)
Defenders: Lukasz Piszczek (Borussia Dortmund), Marcin Wasilewski (Anderlecht), Jakub Wawrzyniak (Legia Warsaw), Marcin Kaminski (Lech Poznan), Grzegorz Wojtkowiak (Lech Poznan), Sebastian Boenisch (Werder Bremen), Damien Perquis (Sochaux)
Midfielders: Eugen Polanski (Mainz), Dariusz Dudka (Auxerre), Adam Matuszczyk (Fortuna Duesseldorf), Adrian Mierzejewski (Trabzonspor), Jakub Blaszczykowski (Borussia Dortmund), Ludovic Obraniak (Bordeaux), Maciej Rybus (Terek Grozny), Kamil Grosicki (Sivasspor), Rafal Murawski (Lech Poznan), Rafal Wolski (Legia Warsaw)
Forwards: Robert Lewandowski (Borussia Dortmund), Artur Sobiech (Hanover), Pawel Brozek (Celtic)