Bale, 29, has been a target for the Bernabeu crowd throughout the season and was again whistled for missing a good chance to score in Sunday's 3-2 win over bottom side Huesca.
That has led to speculation that Bale could be on the move in the summer, with agent Jonathan Barnett telling ESPN FC that the Wales international would "wait and see" before deciding his future.
But speaking at a news conference, Zidane said he could deal with the negative reaction.
"I was whistled too," Zidane said. "You must have the personality to accept what the fans think.
"The players here have the character to deal with it. It is a difficult season but, when things were going well, the fans were supporting us all."
"The players who are here must be respected," the coach said. "To talk of a clearout, for me, is a lack of respect.
"I will confirm -- there will be changes, but this is not the moment to talk about that. We will have time for talking after [the season]."
Zidane, back for a second spell in the Bernabeu dugout, said plans were being made for summer signings, with PSG's Kylian Mbappe and Manchester United's Paul Pogba among the reported targets.
"We are already doing that [planning], although things will be made public at the end of the season," he said. "I am Real Madrid coach, so I have a say.
"But there is an institution here, this is an important club, with people in charge. Things are done collectively."
Asked about reports that defender Raphael Varane had told teammates he wanted to leave, Zidane said: "He has said nothing to me.
"I want him to stay. Things can happen in life, but he looks good to me. The important thing is what he says to me, and he is currently at the best club in the world. He has won a lot here."
Zidane also praised Marcelo, who has returned to his team, saying: "What he has done here as a player has been phenomenal.
"Then, if you play a bit worse, there is a lot of debate. He is a good player and we always ask more from him. He has been questioned a lot lately, but I want him to play many games from here until the end of the season."