The 19-year-old, one of Beckham's five children with former Spice Girl and fashion designer Victoria, made his debut for the American third-tier club in their 2-2 draw with South Georgia Tormenta on Sunday.
Beckham played alongside Harvey Neville, the son of Inter Miami's head coach and ex-Man United defender Phil Neville.
Neville and Beckham were team mates at Premier League club Manchester United.
And Sciaretta said that the youngster showed glimpses of great promise in the match, though he conceded that there's a long way to go for the teenager.
"He's playing in the same position as his father, out on the wing," he told Hawksbee and Baker.
"You could tell he's been in and around the game for a while. He set up some pretty good chances.
"It's a low level but a good starting point for him. It was a good debut so we'll see where it takes him.
"It's a long way between that and the first team. It's several divisions down from the MLS, but he's young and has time on his side.
"It's a good starting point so we'll see where he goes from there."
Asked if he looked out of his depth, he added: "No. When you're making these big appearances and all eyes are on you, you have this jolt of energy.
'You can be a bit cocky and eager but when you get into the grind of things, game in, game out, that stuff goes away.
"It's an exciting thing. He held his own and played well and now it's about seeing how he can do when the eyes are off of him."
After the match, Beckham Jr. said he was 'blessed' to have made his debut.
"Blessed to have made my pro debut," Romeo said in a post on Instagram with a photo of himself in the number 11 jersey.
"Full focus on to the next match."