Menzo had been at the Amsterdam club for a few years. When Cruyff took charge, in 1985, he was an understudy, and had only played a few matches.
Under the Dutch legend's guidance, Menzo went into the first team, aged 21. Cruyff moved on to Barcelona three years later, but the young goalkeeper would keep his place for seven seasons, a star of the side that won the Cup Winners' Cup in 1987 and the Uefa Cup in 1992.
Over the course of a 16-year career in football, Menzo also won nine domestic league and cup titles across the Dutch game and in Belgium, achieved with a style that helped change what many thought a goalkeeper could be. He was an extra man who could do more than keep the opposition out - an early example of the 'sweeper keeper'.
But those years at the top were tough.
Born in Suriname in 1963, Menzo moved to the Netherlands when he was six years old. The racist abuse started early in his career. By the time he was at his peak, it reached a horrible intensity - public, frequent and large scale.
In many of the games he played, there would be monkey chants, racist taunts, bananas thrown on to the field.
"It hurt, it hurt me very hard," Menzo says now. "When you have half the stadium abusing you, it feels very lonely. When I think back, I can't imagine how I did it - how I played my matches."
Racism was such a regular feature of Dutch football at that time that almost nobody talked about it - including those who were being targeted, Menzo says. Even though he tried not to let it affect him, it made him question himself.
"We never spoke about what was happening because we didn't know how to deal with it," he adds.
"Some players said they didn't hear it. I can't imagine that - I heard it always, even when it was one person. It was normal - it became normal.
"I thought it was maybe my personality that made me feel and hear it, and maybe I wasn't strong enough for professional football."
But Menzo did show strength. And on more than one occasion, he physically stood up to his abusers.
The first time was in November in 1987, still early in his Ajax career, at the age of 24. It happened after yet another away game in which he was targeted.
He was coming out of the dressing room and walking across towards the team bus, carrying a box. A young man approached him. He asked Menzo if there were bananas in the box. Menzo put the box down on the ground.
"I said 'what did you say?' and he said it again," Menzo continues.
"At that moment I was not myself, I think, and I hit him.
"The first feeling was just a relief, it was like the pressure fell off me. Throughout the game the abuse was there, and here after the game again too. Now it was - boom."
Menzo struck the man full in the face. His abuser walked off, with a bloody nose and a broken tooth.
The whole incident was witnessed by the opposition team's manager, who defended Menzo when reports emerged in the press. That's how his mother found out what had happened. According to Menzo's biography, she reckoned the abusive young man would have lost more than a tooth if he'd said it to her.
There was no comeback from the authorities - but then little or nothing was done to try to stop the racism regularly aimed at the goalkeeper, either.
Later in his career, when he was playing in Belgium in the 1990s, yet another banana was thrown in his direction.
This time, instead of ignoring it as he had so many times before, Menzo picked it up, peeled it and took a bite. The result was laughter - a lifting of the tension.
"It was a good reaction," he says. "It made me feel good and it gave a positive reaction to the fans."
But Menzo also believes that part of the reaction came because he was older, better known and more respected by that time. As a younger man, such a reaction would have been impossible, he says now.
Stanley Menzo poses with the Ajax team of 1992-93 for that season's team photo
Menzo, standing behind a young Marc Overmars with the Ajax team of 1992-93
It is more than 20 years since the former Ajax, PSV and Dutch international goalkeeper called time on his playing career.
He was collaborating on a book about his life, with journalist and author Mike van Damme, as the Black Lives Matter (BLM) campaign reached new global relevance in 2020, following the murder of George Floyd.
For Menzo, the contrast between the 1980s and 90s and the present day could not be clearer in terms of how football confronts racism. Players speak out. Officials and governing bodies run campaigns. He says he "can't imagine" teams walking off the pitch in protest back in his day.
The problem is far from resolved, but Menzo sees progress.
"What I enjoyed about the BLM discussions was that I didn't see black people demonstrating against racism, I saw black and white people. And that's the whole issue," he says.
"If I feel it as a black person, see it and hear it. Do you see it and hear it as a white person? If not, then we have a problem. If yes, then let's solve it together.
"In football we can change things and… we can use football to change things."
Stanley Menzo, pictured in 2018
Menzo was appointed technical director of the Aruba national team in 2021. In June, they won a match for the first time in three years - beating the Cayman Islands 3-1
It has taken a long time for Menzo to appreciate what he achieved in football. Not just because of the constant abuse that he faced, but because he was often worrying too much about his performances to enjoy success.
"Most of the time I was only seeing the negative things, the goals that I couldn't save," he reflects.
"I was too busy with those things, and forgot to see the positives."
That feeling continued, he says, until he came to collaborate on the book. Its title is Menzo: The Battle Under the Bar.
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