Blaszczykowski's superb strike and a counter-attacking second-half performance earned the hosts a point against a team who had looked like one of the tournament's favourites in hammering the Czech Republic 4-1.
"I am really satisfied after this game," Blaszczykowski said. "We showed what character we have.
"With the sort of support we had here today from the fans, we are capable of achieving a lot. I believe that we can secure a historic advance to the quarter finals against the Czechs."
Coach Franciszek Smuda refused to be drawn on how he would approach Saturday's game in the southern Polish city of Wroclaw, just miles from the Czech border, but signalled he was concerned by injuries suffered by Damien Pequis and Eugen Polanski.
The Poles need to beat the Czechs to qualify for the quarter-finals.
"We will need to wait and see with the players who are injured, whether they are just niggles or something more," Smuda said.
Smuda also said he felt UEFA's decision to open the national stadium's roof for Tuesday's game had helped the Poles and said that the team had felt less under pressure than in the tournament opener.
But he refused to sign up to an enthusiastic reaction from local media, declining to call it the best performance of his two years as coach.
"I think that we have played a lot of good games," he said.
"When you are building a game, you do not play always the same. What I can say is that we can see that the team is playing better and better."
Blaszczykowski said the Poles, who did not have to qualify for only their second ever appearance at the European Championship, had proved their right to be in the tournament.
"We proved that we know how to play, we have character and charisma. We are still in the game, we have two points. For us this is a very positive thing," he said.