Madrid visit Salamanca, who play at 4,000-capacity Las Pistas - a ground which was covered in snow on Tuesday.
Wednesday's match is a huge clash for the Segunda B side and Zidane is fully prepared for a tough evening.
However, the Madrid head coach insists playing at such a small venue and on a difficult pitch will be nothing new for Los Blancos' star-studded squad.
"We have to be totally concentrated, we have to do what we've been doing until now. We have to be ready for the game," Zidane, who confirmed Gareth Bale and James Rodriguez will be available, told a media conference.
"Our players have started out playing on pitches like this, me as well. Difficulties out on the pitch that you're not used to. Mentally we're prepared and in a sporting sense as well.
"We know where we're going to play and what to expect. Perhaps it's 10 or 15 years ago but we've all played on pitches like this, so we're prepared.
"We have to do what we have to do. We have to be ready, it's a cup game and we have to give everything. We know the situation, know where we're going to play, but it's a game of football and our duty is to be ready.
"We're like that not just in every game, but every training session. From day to day we have to be ready for these types of games. It's a very important game."
The Copa del Rey used to have two legs throughout each round but its schedule has been reduced, with the tournament changed to a single-match format until the semi-finals.
"From my experience in France it was always one game and that's it, so my custom is to play one game," Zidane said, when asked if the new format left Madrid with less margin for error.
"Now it's here in Spain and we have to accept that, it's one game and out. So you have to accept it and go and play it like that."
One player who seems unlikely to be involved on Wednesday is Alvaro Odriozola, with the defender having reportedly not trained amid reports he is about to join Bayern Munich on loan.
Zidane did not reveal which clubs are interested in signing Odriozola, but he confirmed the full-back could leave Madrid this month.
"He has an option to go and play elsewhere but nothing is official yet, we're going to wait and see," said Zidane, who may consider recalling Jesus Vallejo from his loan at Wolves.
"The option of Alvaro going is a possibility, it's not official. I'm not going to get rid of one to sign someone else. We've got a big squad and an option could be [bringing back] Vallejo but we don't know yet."