Coach Franciszek Smuda said Poland were "paralysed by the pressure" as Greece fought back from a goal down to draw 1-1 in the opening match of Euro 2012.
Robert Lewandowski gave the co-hosts the lead before Greece, who were down to 10 men before the break, equalised after the interval.
"We were under great pressure, great stress," said Smuda, whose keeper Wojciech Szczesny was also sent off.
"Some of the players were paralysed by the pressure."
Poland coach Smuda added: "I congratulated all the players when they came off and told them to cheer up because it would have been much worse if we'd lost - 1-1 is not the end of it; this tournament is still open.
"We have two matches to go and should not dwell on this but just focus on the next one and winning it."
Poland were fortunate not to lose the match when, with the scores at 1-1, Szczesny conceded a penalty and was shown a straight red card after he had fouled Greece goalscorer Dimitris Salpingidis.
But Szczesny's replacement, PSV Eindhoven keeper Przemyslaw Tyton, came to Poland's rescue when he pushed away Giorgos Karagounis's spot-kick with his first touch.
"During the training camp in Austria, we had a lot of sessions where we took penalties. Lukasz Fabianski, who's injured, is great at stopping penalties but Tyton has made some spectacular penalty saves at club level too," added Smuda.
Greece coach Fernando Santos said his side, who have now only lost once in 22 matches, "showed their character" in the second half.
"The players started the second half very well," said the Portuguese manager.
"They showed their character, they scored a goal. We had another chance to score the second, which would have decided the match, I think.
"Unfortunately, we couldn't score, but that's part of football. In the end both teams were tired but both tried to win, both tried to create chances, and we had the best of the second half."