Poland were in charge right from the start as they pinned Northern Ireland back in their own half and were eventually rewarded when Arkadiusz Milik found the net after the interval.
O'Neill feels his side did well to keep their chances of salvaging a draw alive right until the final whistle, but acknowledged they did not deserve a point.
"It was a very difficult game. Poland were excellent. We were overpowered by the physical strength of the Polish team. We tried everything after going behind, but we didn't create anything. The better team won," O'Neill said at a news conference.
"We did not come into this tournament thinking we would be disgraced. Some of the players could have done better, but they all worked hard. We didn't get the ball quick enough into the final third and did not create enough. Delivery from set pieces was not good enough.
"We did not set the team up to create a gap between striker and midfield. That happened because we were under pressure. We ended with two strikers because we wanted to get it into the box quicker. But it would have been difficult to start like that. We have to recognise the quality of the opposition. You can only go for it if you have the ball. We had to play sensibly."
Northern Ireland face a tough task to progress following Sunday's defeat, but O'Neill refuses to throw in the towel just yet.
"We now have to find a way to get something from the final two games. We will face an equally stiff test against Ukraine on Thursday. We take from today's game that we had a chance of getting a result right until the final whistle. The players gave everything possible," he added.
O'Neill's men did well to keep Robert Lewandowski quiet, however, the Northern Ireland boss was nonetheless full of praise for the Bayern Munich striker.
"Milik was not necessarily a bigger threat than Lewandowski. We knew the danger of all of them. Lewandowski is the one where your defenders can never let up. He is the one who creates room for players like Milik. The fact that he is willing to work for the team shows his class," he continued.
"Poland's biggest threat is obviously Milik and Lewandowski. I was also impressed by [Bartosz] Kapustka.
"Poland will be a good test for any team. They might have difficulties when they are not in possession against the top teams in the tournament."