Butler hit the post for the Royals in the first half whilst Darren Wrack gave Pardew's side a scare when his stoppage time free kick hit the crossbar. The result means that both sides will be in the pot for tomorrow lunchtimes fourth round draw.
The Division One sides must now replay a week on Tuesday at the Madejski Stadium to see who will make it to the round.
Alan Pardew was a little disappointed his side did not win having dominated the game and created the majority of the chances.
"A draw was the least that we deserved, we were the better side. It was difficult for Walsall on that pitch. They were the home team and wanted to get it down and play, but they couldn't," said Pardew.
"I thought we played as well as we could have on that pitch. I thought we passed the ball well at times and the players were a credit to Reading Football Club.
"You could see that our confidence levels were probably higher than theirs, and I'm a bit agreived that we haven't won the tie because we've got it all to do at our place."
Meanwhile, Pardew thought his side could have had a penalty, claiming that following Butler's shot that hit the post Walsall defender Zigor Aranalde blocked Jamie Cureton's follow-up on the line with his arm.
Aranalde's block was sensational, all the crowd sure that the ball was goalbound.
"Aranalde handballed it, that was how he saved it but the ref didn't see it. I thought the ref was excellent today but we all make mistakes."