Nadal, who has won 22 Grand Slam titles, added that the future of Spanish tennis was in good hands with the youngster. Alcaraz has already won majors at the U.S. Open and Wimbledon and is ranked number two in the world behind Novak Djokovic.
"It's a good thing that as a player I will not face him many times," said Nadal, who expects to retire in 2024 after a series of injuries limited his appearances on the circuit.
"As a fan, I will enjoy watching him for many years hopefully.
"In Spain, we should be very, very happy about having someone like Carlos coming.
"He's an amazing player. He's only 20-years-old and he's already won two Grand Slams and a couple of important tournaments."
Nadal, who spent almost a year on the sidelines with a hip flexor injury before suffering a muscle injury at the start of this season, said he felt "much better than expected" during the exhibition match.
Nadal and world number two Alcaraz are next in action at the Masters tournament at Indian Wells.
