Rain lashed down for three hours yet the pitch remained open to the elements - and the match, scheduled to kick off at 8pm UK time (9pm local), was called off at 8.55pm (UK).
The match will be replayed at 4pm UK time on Wednesday.
Quizzed on what he had been told regarding the roof remaining open to the elements, England manager Roy Hodgson told ITV: "I can't answer that, it's not as easy as that. You'll have to speak to the Polish authorities.
"I'm rather hoping they'll get it closed as quickly as possible and do some work on the pitch... if it is to be playable tomorrow afternoon."
He added: "It was pretty obvious to me early on that this game was not going to be played. But I understand the referee wanted to examine every possibility."
The roof was eventually closed, with the ground staff tasked with making sure the pitch is playable by Wednesday.
England officials managed to persuade FIFA to replay the match on Wednesday despite Poland's preference for a later date as their domestic league has fixtures planned for Friday evening.
"At international level the days are not available, they are taken up," added Hodgson. "Poland will unfortunately have to pay the price for that (the roof debacle) because it will be more difficult for them to get the crowd into the stadium in the afternoon.
"We're disappointed as we've prepared well for tonight - although no doubt the Poles have too. We'll have to do it all over again tomorrow."
His Polish counterpart Waldemar Fornalik wanted to move the match to mid-November but was resigned to playing on Wednesday.
"You can play on any pitch, but the question is how such play would look," he said. "I am surprised that after such a rainfall the pitch was in such a state."
A Polish FA spokeswoman said neither of the team representatives nor the FIFA delegate wanted to make the decision to close the roof.
"None of the sides wanted such a solution," said Agnieszka Olejkowska. "We knew there would be heavy rain but we could not 100 per cent predict the downpour."
Then she sought to explain FIFA's reluctance to call the game off even when the situation seemed hopeless: "We have a heating system which, if we close the roof, can dry the pitch in 30 minutes."
A spokesperson for the National Sports Centre, which operates the 58,000-seater stadium built to host the European Championship in June, said: "There is a functioning drainage system but with this amount of rain falling continuously, no system could get rid of this amount of water."
With the stands full of irate home fans, England's travelling supporters cheered every time referee Gianluca Rocchi threw the ball into the air and watched it plop down on to the sodden turf during a pitch inspection at 8pm (UK).
It was difficult to see anything being done to get the match on, with the roof remaining open as the heavy rain apparently prevented it from being closed.
With no ground staff in evidence, FIFA said that it would do everything in its power to get the game played despite the home fans leaving their seats in droves.
As the farce continued, FA director of communications Adrian Bevington said: "There's two things to this: clearly there's a huge problem there for the supporters who have travelled all this way, and the Polish fans who have travelled around their country.
"But likewise, you have also got to take into account the safety of the players, and that pitch tonight was no way playable from a safety point of view."
His view on matters was evidently sensible as a pitch that was relaid less than a week ago after a series of summer gigs - including Coldplay - and was cut up during Poland's friendly win over South Africa at the weekend barely soaked up the precipitation that continued to fall.
Some of the Polish fans that remained entertained themselves by entering the pitch and sliding belly-down into the puddles with stewards in pursuit, much to the amusement of supporters of both teams.
And following a further inspection at 8.45pm (UK), the news everyone expected filtered through: the game could not go ahead.
"We were made into a laughing stock," said former Poland international Tomasz Iwan.
When the sides meet on Wednesday, England will be aiming to maintain their long unbeaten streak against Poland and their place at the top of qualifying Group H.
Hodgson said he would pick the same team for Wednesday, and hoped his players would be as well-prepared as they had been on Tuesday.
The manager, though, was not likely to be fazed by the inconvenience. Asked if he had experienced a late postponement before, the 65-year-old said: "Funnily enough, yes. In 1987, when my Malmo team were all set to play Ajax, a snow storm came in and covered the pitch in snow and caused the game to be postponed for a couple of days."
UKRAINE 0-1 MONTENEGRO
Montenegro joined England on top of the Group H qualifying table with a surprise 1-0 victory in Ukraine as the home team's hopes received a serious jolt on Tuesday.
Dejan Damjanovic scored the only goal in the 45th minute in Kiev after good work down the right by Stevan Jovetic.
Jovetic then missed a golden chance to make it 2-0 when his scuffed penalty was saved by keeper Andriy Pyatov after Evhen Selin brought down Miodrag Dzudovic 10 minutes from time.
Ukraine defender Oleksander Kucher and Montenegro keeper Mladen Bozovic were booked for brawling during a break in play.
The hosts were without coach Oleg Blokhin after he had an operation last week to treat thrombosis.
It was due to be Blokhin's last game in charge before he takes over as coach of Dynamo Kiev on a full-time basis.
Montenegro have seven points from three games, level with group leaders England.
Ukraine have two points and are third from bottom.
SAN MARINO 0-2 MOLDOVA
Moldova joined Poland on four points as they beat minnows San Marino 2-0 in Serravalle.
However they had to wait until the 72nd minute to take the lead, Serghei Dadu converting a penalty.
Alexandru Epureanu doubled their advantage on 78 minutes.