Poyet said: "We can go there and enjoy it. If we play our game and they don't, who knows?"
The pitch at the Banks's Stadium was only declared fit to play a few hours before kick-off because of the melting of snow and heavy rain overnight.
And Poyet added: "I told my players there would be no excuses. This is England and this is the weather. The Walsall staff had worked very hard to get the game on and everybody wanted to play.
"We had to defend in the second half and credit to Walsall for the way they tried to save the game, and had a chance to equalise right at the end."