Ferrero, a former world number one, has worked with 19-year-old Alcaraz since he was 15 and overseen his rapid rise to the top of the game.
That was capped on Sunday when he defeated Casper Ruud in the US Open final to win his first grand slam title and become the youngest men's world number one in history.
Ferrero looked on proudly from the stands at Flushing Meadows and then made no attempt to play down the proclamations of greatness being bestowed on his charge.
"Carlos, I think he was born to play this kind of tournament, born to play these kind of matches," said the Spaniard.
"Since the moment that I started with him, I saw some things that were different than the other guys at his age. I am still seeing it on the court. In important moments, he always tries to go (for it).
"This is one of the more difficult things in tennis, even in his first grand slam final. He's a great competitor. He's there. He's trying all the time."
Alcaraz expressed surprise that he was able to win his first grand slam title so quickly, but Ferrero, the French Open champion in 2003, was not shocked.
"No, because I know his level," he said. "Of course, it comes very fast. It's a surprise for everybody except maybe to me because I trained with him every day and I know what he's able to play on the court.
"I was pretty sure that maybe if it wasn't this year, could be the next one. I'm very happy about it. It was fast, but now definitely we want to continue."
There are quirks to Alcaraz's position at the top of the rankings, such as the decision not to award ranking points for Wimbledon and Novak Djokovic not playing the Australian Open or US Open, but no one within tennis is questioning whether he is the real deal.
The 19-year-old has no apparent weaknesses in his game and his competitive desire was evidenced by the three late-night five-set matches he played to reach the final.
Ferrero still feels there is plenty Alcaraz can improve, though, saying: "I think he's on 60 per cent of his game. He knows and I know that we have to keep working.
"Once you get to the number one, it's not done. You have to keep working, keep playing at a huge level to keep winning.
"The players now, they're going to play very motivated against him. It's like Real Madrid-Barcelona, there's a rivalry that gets you to increase your level. He has to be ready."
Alcaraz's movement has wowed more than anything, with the teenager tracking down seemingly impossible shots and maintaining his speed and stamina through epic matches.
Ferrero said with a smile: "When he arrived to the academy when he was 15, he was like spaghetti. We had to work. Obviously we saw that he had very fast hands, very fast legs, but no muscles at all, not in the back, not in the legs."
Beaten finalist Ruud, who now sits behind Alcaraz at number two, believes the teenager is a combination of Rafael Nadal and Djokovic.
"He's very fast," said the Norwegian. "He's a great mover. He can get to balls that we've probably never seen before.
"Rafa, when he was Carlos' age, he was also similar. He tracked down everything. Novak, the same with his flexibility. He gets to certain shots that you think, 'How is that even possible?'
"Carlos has sort of a mixture of both. He's fast, flexible. He can slide around. It's impressive. He's a hard nut to crack."
Having won three grand slams between them this season, it would certainly be premature to write off Nadal and Djokovic yet, but the US Open was a glimpse into tennis' future.
Ferrero cited 21-year-old Jannik Sinner, against whom Alcaraz saved a match point in the match of the tournament in the quarter-finals, as the player he expects to be his man's biggest rival.
"Sinner and Carlos could dominate the tour for maybe the next 10 years, from what I saw the other day," he said.
As for whether Alcaraz can eventually rival the extraordinary records achieved by Nadal, Djokovic and Roger Federer, Ferrero added: "I have the goal to put him on the high level of tennis.
"Of course, I think it's going to be very, very difficult to achieve what they have done. We're talking about 22 grand slams. He has only one. It's a long way still to go.
"But who knows? I think he has all the tennis and potential to be one of the best. All we have to do is try it."