Reigning Champions Real sit third, 10 points behind leaders Atletico Madrid but having played a game more.
And a poor recent run has led to media scrutiny over the French manager's position at the club.
"What makes me laugh is you ask me why I might be annoyed," Zidane said in a news conference on Friday.
"I don't deserve to be treated like that by the press. We won the league last season and I'd hope for a bit of respect.
"We've earned the right to fight for La Liga this season, at least give us the season. Next season, there'll need to be changes, but this year let us, the team who won the league last season, fight for it this year, too.
"It wasn't 10 years ago, it was last season. Just show us a little bit of respect for what we've achieved. You [the press] say a lot. Why don't you tell me to my face that you want me out of the club, not just behind my back."
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