Wayne Rooney's header via his shoulder from a Steven Gerrard corner just after the half-hour mark put the visitors ahead but defender Kamil Glik levelled for the Poles, also heading home a corner with 20 minutes remaining.
"It's my fault. That's cost us three points," England goalkeeper Joe Hart told ITV television after failing to get any contact on Ludovic Obraniak's corner which was nodded in by Glik.
"It's a decent point but we know we can play better than that. I believe this point will be a good one at the end of the day, I don't think any team will get maximum points here," said England captain Gerrard.
The match had been scheduled for Tuesday but was postponed due to a waterlogged pitch when officials failed to close the national stadium's roof despite a heavy rainstorm, angering thousands of fans who were kept in the arena for hours.
"The fans were outstanding staying an extra day. Their fans were great coming too. We made something good out of it," said Hart.
Poland tried hard to inflict a first defeat on the former World Cup winners in nearly 40 years and after Glik's equaliser the momentum was with the home side but England held out.
"I feel disappointed. We had a chance. We could have won. But congratulations are in order to the team anyway," said Polish captain Jakub Blaszczykowski who missed the game through injury.
