The Latics reached the fifth round of the competition last season after recording wins over Nottingham Forest and Liverpool, but Johnson wants his team to be solely focused on their encounter with Wolves at Boundary Park.
The 32-year-old told BBC Radio Manchester: "We all think about another cup run, but we've got to take this game as it is. It's a tie in the first round, and it's a tough game.
"We've got to get the boys thinking about that and nothing about the future."
Johnson has guided Oldham to 17th position in the League One table this season.