The La Liga champions were put to the sword by Manchester City at the Etihad on Friday night.
Two errors from Raphael Varane proved to be the defining moments of the game as Raheem Sterling and Gabriel Jesus made it count for the hosts.
Zidane, in the process, lost a Champions League knockout tie for the first time in his coaching career but was not left disheartened and believes Real Madrid have to be proud by referencing their La Liga triumph as their season’s high.
“When you lose you can't be happy," the French coach said afterwards. "But we have to be proud of what we've done.”
"We have to congratulate our opponents because they played well.”
"We don't have to look for excuses, we lost both games, but the most important thing is that I'm proud of this team.”
"We've done all we can on the pitch, but sometimes it doesn't work out.
“We can’t be happy obviously, we have lost the game and we are out.
"We are proud of what we achieved this season, this is football. We lost to a good team and have to accept it. We had our chances to score.”
"95% of what we achieved this season has been excellent. We have to accept this. We need to be very proud of what we have achieved."
Zidane was asked about his future in Madrid and he quickly quashed every potential exit claims.
"I am the Real Madrid manager until something happens out of the ordinary.”
"You don't need to ask any more questions about my future. We will all have a rest and come back again next season."