Despite exiting the Copa del Rey due to fielding an ineligible player, Real is still into the last 16 of the UEFA Champions League and just four points behind Spanish La Liga leader Atletico Madrid.
When asked what would make him happy at the end of the season, Zidane replied: "Win everything.
"We have the possibility to win La Liga and the Champions League and we will aim to win both.
"There is room for improvement. We're still near the top in the league and are in the Champions League. We must be positive."
He is widely regarded as one of the greatest footballers of all time, but will "Zizou" cut it as a coach?
The French icon, who inspired his country to World Cup glory in 1998, took over as head coach of the Spanish giants following the sacking of Rafael Benitez on Monday -- becoming the club's 11th boss in just 12 years.
Benitez always faced an uphill battle to win over Real fans, with his preferred style of football not akin to the fast, attacking play synonymous with the club over the years.
Zidane, however, seemed keen to appease supporters and sounded certain as to how he wants his team to play.
"Good football has always been important here," he said. "Good football, beautiful football and I will continue with this; attacking but with balance.
"We will work hard to be the best on the pitch. I've seen a focused team, switched on and all happy."
It is no secret that Real club president Florentino Perez desires to emulate Pep Guardiola's success at Barcelona, and given Zidane and the Catalan's similar rise from player to youth coach to head coach, comparisons between the two have already been drawn.
"You shouldn't do the comparison (between me and Guardiola)," Zidane said. "Guardiola is Guardiola. He is a fantastic coach and what he is doing is impressive, but I'm not going to compare myself to him.
"I never did it as a footballer and I will not do it as a manager. I will try to do everything possible to work hard.
"I've known (Jose) Mourinho, (Carlo) Ancelotti and Pep and worked under lots of coaches, and I'll choose parts from all of them. But I need to be the coach I want to be.
"I'm going to try and add something personal to this team and want my style of football to be different, to be positive with balance. "
Sunday's 2-2 draw with Valencia proved to be Benitez's last game in the charge of the 10-time European champion -- which sits third in the Spain's top division.
Perez confirmed Benitez's seven-month tenure as coach had been terminated at a press conference at the club's Bernabeu Stadium Monday before Zidane briefly addressed the assembled journalists.
"Firstly I would like to thank the club and the president for giving me the chance to coach this team," Zidane said.
"We have the best club in the world and the best fans in the world," he added.
While those Real fans never really warmed to Benitez, who replaced the popular Ancelotti in June last year
, they adore Zidane.
Signed by the club in 2001 for a then-world record fee of €75 million ($81m), he scored one of the most memorable goals in football history as Real defeated Bayer Leverkusen in the 2002 UEFA Champions League final.
During his time at the club Zidane, who previously played for Cannes, Bordeaux and Juventus, also won the Spanish La Liga title, UEFA Super Cup, Intercontinental Cup and Spanish Super Cup. He was crowned FIFA World Player of the Year on three occasions.
He enjoyed European Championship success with France in 2000, alongside the World Cup win in 1998, although his career ended in controversy -- infamously headbutting Italy's Marco Materazzi
in the 2006 World Cup final in his last professional game. France went on to lose the match on penalties.
Since 2014, Zidane has coached Real Madrid Castilla, the club's B team which plays in the third tier of Spanish football.
The team missed out on promotion in his first campaign in charge, while he departed with it in second place in the division.
First brought back to Real as an adviser in 2009, Zidane was Ancelotti's assistant coach during the 2013-14 season, when the club won La Decima -- its 10th European Cup.
Zidane, whose four sons are all part of Real's youth setup, will take charge of the senior side for the first time Saturday against Deportivo La Coruna at the Bernabeu.
His appointment was hailed by former Real teammate David Beckham, who took to Instagram to express his delight at the move.
Former Liverpool coach Benitez endured an uneasy relationship with Real's fans, not helped by November's crushing 4-0 defeat to archrival Barcelona
, while the club's expulsion from the Copa del Rey after fielding an ineligible player did little to ease tensions.