Leverkusen returned to the Bundesliga's top four on Saturday with a 1-0 win over Freiburg, building on their 1-0 victory over Atletico Madrid in the UEFA Champions League three days earlier.
Kaiserslautern are their opponents in the next round of the cup on Tuesday, and Schmidt is keen for Leverkusen to continue their impressive form.
"We are in good shape and are aware of our strength at home," said the head coach.
"It is hard to say how they will perform against us, but Kaiserslautern has put in many high-intensity performances. We are prepared for everything.
"The cup has traditionally been a high priority in Germany. The incentive to go far in the competition is enormous, I have a good feeling."
Victory would see Leverkusen make the last eight of the competition – that they won for the only time in 1993 – for a second successive season.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.