Bale joined Real two-and-a-half years ago for a world record transfer fee but has struggled at times in the Spanish capital.
Despite renewed interest from Manchester United, the 26-year-old was thriving at Real under Rafael Benitez and Zidane moved quickly to reassure Bale that the former Chelsea and Liverpool manager's sacking would not affect the Welshman.
"I can understand that he might feel aggrieved by Benitez's departure but I will show him the same affection that he had from Rafa," said Zidane at his first press conference as Real coach, just a day after being appointed by president Florentino Perez.
Zidane to be 'top-class manager' - Houllier
"He's a vital player for the team."
Zidane, a former star player with Real whose stunning winning goal against Bayer Leverkusen earnt the club the 2002 Champions League, played down comparisons between himself and Pep Guardiola, the former Barcelona coach.
Guardiola was also a star player in the Catalan capital before becoming their most successful coach ever during a trophy-laden four-year spell in charge at the Camp Nou.
"Guardiola is Guardiola, he's an incredible coach but I'm not going to compare myself to him," said the 43-year-old Frenchman.
Madrid fans allow themselves to dream as Zidane takes charge
"You can't do the same thing as another coach, I must do Zidane."
Earlier in the day, thousands of fans had turned out to watch Zidane take his first training session with Real's current 'galacticos', including Cristiano Ronaldo, Bale and Karim Benzema.
Zidane is tasked with lifting the club out of its year-long slump that has seen them burn through two Champions League-winning coaches -- Benitez and Carlo Ancelotti.
They are in third place in La Liga, four points behind leaders Atletico Madrid and two points behind eternal rivals Barcelona, who have a game in hand.
Madrid were recently booted out of the Copa del Rey for fielding an ineligible player, but they are still in the Champions League, facing Roma in the last 16 next month.
And Zidane insisted that his aim was to win a trophy.
"This is a difficult but stimulating challenge, I want to take up the challenge and do my utmost to win titles," he told reporters.
"I'm at the best team in the world," said the Frenchman, who played for the club between 2001 and 2006.
"Our objective is to win, we have two titles that we can win and we will try," he added in reference to the Champions League and La Liga.
All eyes will now be on whether Zidane has the temperament and tactical ability to gel Madrid's 'Galacticos' into a trophy-winning unit.
Key players such as Benzema and James Rodriguez often showed their disgust when substituted by Benitez.
Off-field distractions also took their toll with Benzema facing blackmail charges over a sex-tape of France teammate Mathieu Valbuena, and Rodriguez accused of speeding at up to 200kph (124mph) last week.
Zidane is not known for his communication skills and had a fiery temperament on the field as a player. His career ended with an infamous headbutt on Marco Materazzi in the 2006 World Cup final between France and Italy.
But unlike Benitez, he is widely thought to be respected by Madrid's players and is certainly adored by their fans.
The man who will become his chief rival, Barcelona boss Luis Enrique, said the change in coaches at Real was to be expected.
"I'm not surprised, it's a regular subject in modern football," said the former Roma coach.
"The chain always breaks at the shortest link and this link is the coach."
He added: "All coaches at some point in their careers are sacked, it's a risky profession."
And Spanish media said that Zidane has his work cut out because of his lack of experience.
He has only spent a season and a half in charge of Madrid's feeder team Castilla, which failed to secure promotion from Spanish football's third tier last season.
But he has the advantage of knowing the players well -- he was Ancelotti's deputy in 2013 and 2014.
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