Earlier this month Klopp announced his decision to leave the German giants after seven successful campaigns in charge of the club.
Dortmund travel to Bayern Munich on Tuesday night for a place in the final of the DFB-Pokal, having won four of their past six matches in all competitions.
"We feel a great sense of gratitude and we owe him," the Japan international told the Bundesliga's website.
"Soon it'll be time for him to go and that won't be easy, which is all the more reason why it's now about us giving even more for the coach in the last few games.
"The Bayern game's coming at a good time for us. We'll be able to take our momentum from the league into the semi-finals of the cup.
"The last few games have given us a lot of belief. That's what we want to draw on in the cup and show in Munich on Tuesday."