Smuda also had a list of seven players that could still be included before the tournament, co-hosted by Poland and Ukraine, starts on June 8.
As expected, Smuda left out Cologne winger Slawomir Peszko, after he was involved in an alcohol-related incident last month, but called up Anderlecht defender Marcin Wasilewski, who accompanied Peszko on the night.
The co-hosts, who are drawn in Group A with Russia, Greece and the Czech Republic, are likely to rely heavily on their trio of Borussia Dortmund players, which include striker Robert Lewandowski, and Arsenal keeper Wojciech Szczesny.
Defender Lukasz Piszczek and midfielder Jakub Blaszczykowski, together with Lewandowski, give the Bundesliga champions a strong Polish spine that Smuda hopes will stiffen the national team in its second appearance at the Euro finals.
Arsenal's 22-year-old goalkeeper Szczesny appears to be the only other clearly established starter for Poland's opening game against Greece.
Lacking local talent, Poland searched far and wide for players with Polish roots.
The squad includes defenders Damien Perquis from Sochaux and Werder Bremen's Sebastian Boenisch, as well as midfielders Ludovic Obraniak from Bordeaux, Fortuna Dusseldorf's Adam Matuszczyk and Mainz's Eugen Polanski. All were either born or raised abroad.
Poland, 65th in the FIFA rankings, are the lowest-ranked nation in the tournament, but the coach believes they can progress to the quarter-finals.
"Our goal is to win promotion from the group, I am convinced we can do it," Smuda said.
"In the last few months we analysed all the teams. Russia has really excellent players, also Greece is a good team. Russia are favourites to win the group, but we are playing at home and we have to do everything to win promotion."
Goalkeepers: Wojciech Szczesny (Arsenal), Lukasz Fabianski (Arsenal), Przemyslaw Tyton (PSV)
Defenders: Lukasz Piszczek (Dortmund), Marcin Wasilewski (Anderlecht), Jakub Wawrzyniak (Legia Warsaw), Marcin Kaminski (Lech Poznan), Grzegorz Wojtkowiak (Lech Poznan), Tomasz Jodlowiec (Polonia Warsaw), Sebastian Boenisch (Werder Bremen), Damien Perquis (Sochaux), Kamil Glik (Torino)
Midfielders: Eugen Polanski (Mainz), Dariusz Dudka (Auxerre), Adam Matuszczyk (Fortuna Duesseldorf), Adrian Mierzejewski (Trabzonspor), Jakub Blaszczykowski (Dortmund), Ludovic Obraniak (Bordeaux), Maciej Rybus (Terek Grozny), Kamil Grosicki (Sivasspor), Rafal Murawski (Lech Poznan), Rafal Wolski (Legia Warsaw)
Forwards: Robert Lewandowski (Dortmund), Michal Kucharczyk (Legia Warsaw), Pawel Brozek (Celtic), Artur Sobiech (Hanover) Substitutes: Grzegorz Sandomierski (Jagiellonia Bialystok), Arkadiusz Glowacki (Trabzonspor), Marcin Komorowski (Terek Grozny), Ariel Borysiuk (Kaiserslautern), Arkadiusz Piech (Ruch Chorzow), Michal Zyro (Legia Warsaw), Ireneusz Jelen (Lille)