Kamil Glik headed in Poland's equaliser in the 70th minute in Warsaw after goalkeeper Joe Hart floundered as he attempted to punch away a corner.
"I didn't get there and the lad has done a good header," Hart said. "It's my fault, I probably should have punched it or stayed in goal. I didn't do either and it's probably cost us the three points.
Wayne Rooney put England in front in the 31st minute, when captain Steven Gerrard's corner bounced off his shoulder and was helped into the net by Lukasz Piszczek.
But as England became increasingly sloppy, Rooney squandered a chance to extend the advantage before Glik's equalizer on a lackluster afternoon for the English in the Polish capital.
"I don't think Wayne was having one of his better days and he was also tiring," Hodgson said.
England, who were also held to a 1-1 draw by Ukraine at Wembley, have a one-point lead in Group H over Montenegro but have played an extra game. Roy Hodgson's side has won two and drawn two.
"We are disappointed not to take three points today," Gerrard said. "Our points tally could be a lot better ... we are not going to grumble."
The team had been forced to wait another day to play after heavy rain on Tuesday — and the failure to close the stadium roof — left pools of water on the field at the 1.8 billion zloty ($600 million) National Stadium.
Hodgson didn't think the surface had fully recovered.
"The pitch was quite difficult, it was a soggy pitch, the ball wasn't moving well," Hodgson said.
England were guilty of needlessly giving the ball away too often when in possession and lacking in creativity, leaving Jermain Defoe isolated up front.
Poland exploited space down England's right flank and Hart had to be alert early on to clear the ball away from the feet of Piszczek.
A poor clearance from Hart straight to Kamil Grosicki also presented the Poles with an opening. Grosicki released Robert Lewandowski, who skipped past the challenge of Cleverley and into the penalty area before firing a cross-shot wide of the post.
But Rooney silenced the fans who managed to attend the delayed match.
"We had a failed cover at one corner kick and that led to a mishap," Poland coach Waldemar Fornalik said. "But in the second half we forced the English into defense."
At the start of the second half Ludovic Obraniak was denied by Hart's only good save, while Piszczek's half volley went wide.
But the equaliser finally came when Hart and Lescott were exposed by Glik.
"We toiled very hard," Glik said. "It was a very tough game, especially when we were losing 1-0 ... (but) our game was consistent, we had a good pace from the start and we kept it in the second half and we scored. England did not create clear scoring situations."