The tie in Warsaw was postponed after a day of torrential rain in the Polish capital and authorities at the National Stadium failing to close the arena's roof.
Large numbers of Three Lions fans had made the trip to the Euro 2012 co-hosts but the players failed to emerge from the bowels of the stadium after the postponement to thank the supporters.
Bevington told reporters: "We have made it clear, frequently, just how important the supporters are to us. These are pretty unique circumstances.
"We had said to the players to get changed significantly earlier than when the game would be called off because we didn't think there was any chance of the match being played, but we didn't want it to look as if we'd made their decision for them.
"There's nothing but respect for those fans who have travelled all that way. There was no disrespect intended."
|WINNING IN WARSAW?
|11/2||England are 11/2 to beat Poland 1-0 with William Hill|
"That has to be the priority. We were not able to confirm anything [about the game being postponed] until we were told ourselves.
"We were asked not to confirm anything until we were told by the referee at 10.05pm. It's extremely regrettable for all supporters who have missed out tonight.
"Hopefully the game goes ahead at 5pm [local time] tomorrow [Wednesday] with supporters in the stadium."
Wayne Rooney tweeted his thanks to fans, and also expressed regret at not being able to greet the travelling support personally.
He tweeted: "Thanks to the England fans who came tonight. Sorry we couldn't come out of the tunnel to see you but we all really appreciate your support."