Last season, Zidane led Real to the La Liga and Champions League double, but the Spanish giants have struggled in both competitions during the current campaign.
Zidane has come under scrutiny at the Bernabeu, but Mbappe has claimed that the France legend - his childhood idol - continues to have the respect of everyone involved in the sport.
The 19-year-old told Marca: "I had Zidane as an idol. But everyone in France loved Zidane. Anyone who likes football knows that he is a special case.
"What he is doing with Real Madrid since he became a coach is incredible, because I know that in that club it's not easy. He's taken a lot of pressure, maybe because he knows the club very well from his time as a player.
"He won the respect of everyone and I'm pleased for Zidane, for everything he's achieved."
Mbappe came close to joining Madrid last summer before opting to sign for PSG, where he has contributed eight goals and eight assists in 14 appearances in Ligue 1.