The League One club are into the FA Cup quarterfinals since 1954.
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After the 1-0 win, Waine told TNT Sports that he had wanted Newcastle United in the next round until their exit yesterday, but says the team will "take it to" whoever they get.
"That is unbelievable, I have never seen this place like this," he said afterwards.
"I know it wasn't the best game to watch but I think we deserved it. We love this pitch here at Port Vale and we played to the conditions.
"We got a chance, we took it and then we dug in and defended for our lives."