Lewandowski opened the scoring before a red card for Sokratis Papastathopoulos appeared to put the hosts in the driving seat.
However, the Greeks grabbed an equaliser through Dimitris Salpingidis before Poland saw their goalkeeper Wojciech Szczesny also red carded - though the subsequent penalty was saved.
And striker Lewandowski rued his side's inability to capitalise on their numerical advantage early on, telling reporters: “I knew that we had to score a second one as one goal is not enough.
“We had good chances in the first half but we could not score the important second goal - there was a lack of concentration and coolness.
“We have not felt any special pressure today. We were very solid in the first half in the defence and Greece could not create any chances. We must show the performance from the first half in the whole game against Russia.”
“Our rivals had a penalty, and we are lucky that they didn’t score.
"Although the Greeks played with ten against our eleven, in the second half we couldn’t make ourselves any situations.
“We were weaker than our first half performance. I hope that in the next matches it will be different.”
Meanwhile, captain Blaszczykowski bemoaned the clinical Greek performance but insisted the Poles will not give up.
“In the second half we wanted to keep the ball longer, which ended in us losing it," he said.
"The Greeks used two of our mistakes – one scored, the second a penalty. But this is football, we cannot give up”.