Defender Damien Perquis headed the winner in the 30th minute - his first international goal - after a pass from Lukasz Piszczek.
"We played well but we aren't yet where we want to be," Perquis told Polish television after the game in Klagenfurt, Austria.
Smuda, who will announce the 23-man squad on Sunday, was forced into one late decision after his number two goalkeeper, Lukasz Fabianski, was ruled out of the European Championships through injury.
Fabianksi, the Arsenal reserve, hurt his shoulder in training at Poland's pre-tournament camp in Austria.
"I picked up the same injury in very similar circumstances the first time at Arsenal [in January 2011]," Fabianksi was quoted as saying on UEFA's website.
"It is the same shoulder. I will undergo some more medical tests next week and hope to hear some good news. I am only hoping that surgery won't be necessary."
Poland have called up Grzegorz Sandomierski as Fabianski's replacement.
Smuda's side will play one more friendly, against Andorra on June 2, before opening Euro 2012 against Greece in Warsaw on June 8.
