The Dutchman has been ever-present throughout the Latics' journey to the last eight of the competition, and is now keen to earn a semi-final berth and a big day out.
"We're coming closer and closer to Wembley now but we'll have to wait and see whether we get Oldham or Everton and then prepare from there," he told the club's official website.
"It is the second time in a row now that we don't know who we are playing yet but it doesn't matter because we have to be ready for anything.
"When the time comes we just have to work hard like we did in the build-up to the fifth round and then who knows how far we could go."
Prior to Sunday, Roberto Martinez's men had not won a game since their last outing in the FA Cup, and Stam insists it is important their cup form carries over to the league.
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"It was great to win the game in the way we did and we're all really pleased to be through to the next round," he continued.
"The atmosphere we have started to create in the dressing room is really good but in the end it all depends on the result and we have to make sure, like today, that we get the results to keep everybody's spirits high.
"We have to win games and when we do what we did against Huddersfield it really gives us the confidence to carry into the next game.
"We all want to take this performance into the next league game which is a higher level but if we play to our own strengths then it gives us a great chance of collecting three points," he went on to say.
"Now it's all about being ready for next weekend against Reading and continuing this winning feeling."