Zambrano was involved in an intense battle with Dortmund striker Robert Lewandowski for the entire 90 minutes of Dortmund's 1-0 win in the DFB-Pokal on Tuesday.
The teams play again on Saturday, this time in the Bundesliga and with Klopp pointing an accusing finger at Zambrano.
"I think Zambrano is an excellent central defender, but he did some things which didn't please us," Klopp said.
"On Wednesday morning, we had a pile of Frankfurt shirts in the dressing room which had been washed and right to the very end, Zambrano's shirt was still lying there.
"I asked, 'Who swapped shirts with Zambrano?'. Nobody replied."
That was only one of the duels in a keenly contested cup game which Klopp expects to be reprised in the league at the Westfalenstadion.
"It felt like a tight game and we deserved to win it, but if we want to do that again, we're going to have to be very strong," said Klopp.
"We didn't beat them last time or the time before that."
Zambrano may be pulled out of the firing line by Frankfurt coach Armin Veh to protect him from a looming suspension.
The Peruvian defender is only one booking away from a ban and a yellow card on Saturday may seem inevitable if he once again has to deal with Lewandowski.
Veh took similar action in a recent Bundesliga game with Bayern Munich, resting the players who risked missing the subsequent clash with Eintracht Braunschweig while naming his strongest team for that match.
He will be without captain Pirmin Schwegler, however, due to a slight fracture to his ribs. He already missed the cup tie in midweek.