Vale won 1-0 thanks to Ben Waine's goal and are into the quarterfinal hat for the first time since 1954.
Aussie manager Brady said at the final whistle: "I'm trying to let it sink in at the moment. It was tremendous form the boys.
"We had to suffer at times but when they pushed toward the end we broke with real pace. Thought we might have had a penalty, then Andre Gray misses one.
"It really hasn't sunk in it. Overall it felt quite comfortable."
On what it means for the club:, Brady continued "We have an fantastic owner in Carol Shanahan. She talks about a football being like a game of snakes and ladders, you can be up or down, she just says that we must stay on the board and I think that is a really good analogy.
"The players are proving themselves and hopefully in the league we can turn our form around."
On goalscorer Ben Waine, he added: "He has popped up with really important goals. He is someone who takes a chance and pops up at the right time."