Lewandowski scored Poland's goal in the first half, only to see Greek substitute Dimitris Salpigidis equalise after the break in a match which saw both teams finish the game with 10 men.
The Borussia Dortmund front man, however, refused to confirm Poland coach Franciszek Smuda's suggestion earlier this week that he would be playing at Old Trafford next season
Lewandowski, 23, said: "I am so happy to score this goal in the opening match. But I'm not going to concentrate on these issues (joining United). Euro 2012 is the priority. I'm totally focused on the national team."
Instead, he rued a string of missed Poland chances which could cost them in Group A, especially missing a first-half header in front of a gaping goal.
He said: "I did everything to take the ball. I was just millimetres away but this is football and I hope next time I score.
"I regret that we did not take more of our chances in the first half. It could have been two or three zero but we still have a positive attitude."
The game turned on two dismissals, Sokratis Papastathopoulis being sent off for two yellow cards in the first half and Arsenal goalkeeper Wojciech Szczesny being dismissed for bringing down Salpigidis in the second.
In the end the Poles had substitute goalkeeper Przemyslaw Tyton to thank for their point when he saved the resulting penalty taken by Greek captain Giorgos Karagounis.
Greek coach Fernando Santos insisted Papastathopoulis was harshly dismissed but refused to criticise Spanish referee Carlos Velasco Carballo.
He said: "When Sokratis (Papastathopoulis) was sent off it wasn't justified but still we succeeded in keeping on the pressure. I totally accept the decision of the referee but it was a difficult situation for us.
"In the end both teams were tired but tried to create chances and we had the best in the second half."
He also refused to blame 35-year-old Karagounis for missing the penalty saying: "He has scored in the past, this is football. My players did a great effort in the second half."
Santos admitted some of his players were tired after a long season and hinted he will rotate his squad over the next two group games against the Czech Republic and Russia.
He said: "We have three games to play in a short time so we have to handle the players accordingly. Some players will not be fit to play two 90 minutes in a few days."