Madrid had one of the worst seasons in their history last time out as they went through three managerial reshuffles and finished third in La Liga, 19 points behind champions Barcelona.
Los Blancos, who went into the season having won three straight UEFA Champions League trophies, were eliminated in the round of 16 stage of the competition by Ajax Amsterdam.
This season has seen the club embark on a massive outlay in the transfer market, bringing in the likes of Eden Hazard, Eder Militao, Luka Jovic and Alphonse Areola for big money.
Speaking at Madrid's ordinary general assembly, Perez said: "This is a united club and that's our strength, the strength of 'madridismo' [Real Madrid fandom].
"We have to understand that this team had won everything there was to win in a unique and historic cycle which saw us lift 17 titles in the past nine seasons. An almost inimitable cycle.
"It's been a difficult season and we've all taken stock where necessary, because we need to turn the situation around. Don't be in any doubt that we will do just that.
"By placing great demands on ourselves, we must carry out the transformation required which will allow 'madridistas' [Madrid fans] to dream of new successes and titles.
"Our challenge is to keep winning on an international football stage which is increasingly complicated and competitive. And of course, we need to recover that hunger for success. The desire that has been a crucial factor in enjoying one of the best eras in our history."
Real Madrid have begun the new season with two wins and two draws, and will start their quest to reclaim the Champions League crown with an away trip to Paris Saint Germain on Tuesday.
