The diminutive Italian forward, who is leaving to play for Serie B side Cagliari in his native Sardinia after seven years spent delighting Chelsea fans with his midfield artistry, dead-ball skills and goal-poaching prowess, said the Russian tycoon had taken on a big responsibility when he bought Chelsea last week.
"Football is not a normal industry, it needs care. It has an important role in society," Zola said.
"Sometimes you have to do things that don't make money but give satisfaction, I hope the new owner understands this.
"He's got a big responsibility on his shoulders. I hope he's gong to do the right thing by the club. They deserve it."
The Italian, brought to the club by Ruud Gullit in 1996, has been a fans' favourite ever since and was voted the greatest player in Chelsea's history in an internet poll last season. He made 312 appearances for the club, scoring 80 goals.
He turned 37 last Saturday after one of the best seasons of his career, finishing as the club's top scorer and top provider.
Manager Claudio Ranieri had frequently described his fitness as phenomenal, saying he trained with the side at scheduled sessions then continued on his own in order to keep playing at his peak despite his age.
"I think he is unique" Ranieri said.
Zola came to prominence under Ranieri at Napoli more than a decade ago, where he was understudy to Diego Maradona and learned many of the Argentine master's tricks, including exceptional ball control and wickedly-curling free kicks.
He won the Italian title with Napoli and the UEFA Cup with Parma but said it was after joining Chelsea at the age of 30 that he really felt fulfilled.
"It is the place where I probably received the most satisfaction of all -- the place where I received everything I dreamed of when I started playing football," the Italian, who played 35
Zola helped Chelsea to two FA Cups, a League Cup and scored the only goal in the 1998 Cup Winners' Cup final in Stockholm.
He was unusual in the premier league in that he was well received everywhere he played. Rival fans enjoyed his artistry, recognised his sportsmanship and often applauded him off the pitch.
Journalists, who voted him Footballer of the Year in 1997, also appreciated his candour and obvious love of the game and he was accorded a rare standing ovation at the end of his farewell news conference on Monday.
To Chelsea fans he could do no wrong. "They gave me everything I was looking for. They made me feel very important even when I wasn't playing well," he said.
Zola would often be seen after matches and long training sessions patiently signing autographs for legions of young supporters.
He said he had hoped to stay in London for another year but could not agree on a package with the club who were severely financially stretched before Abramovich pitched in with his oil wealth.
Zola agreed to a deal with Cagliari and stuck to it despite Chelsea, suddenly buoyed by Abramovich's millions, coming back with the offer of a new contract. "I spent a couple of very bad hours," Zola said. "But I had agreed to go and I could not go back on my word."
Cagliari, bidding to return to Serie A had been chasing Zola for several months.
"I want to go back where I started from and try to give something back," he said.
Zola has not abandoned Britain, however. He and his family are keeping a house here and he is arranging a friendly fixture between the Chelsea and Cagliari.
"You are going to continue to see my little face here. We will come back often," he said.