Garnacho assisted United forward Joshua Zirkzee's debut goal in their 1-0 league opener win against Fulham and scored in the Community Shield against Manchester City, which United lost on penalties.
The Argentina international, alongside Kobbie Mainoo, also scored in United's 2-1 FA Cup victory over City and provided many bright moments with seven league goals in United's lacklustre season, as they finished eighth.
"To make that jump to being a world-class player, he has a long way to go. It starts with hard work," Ten Hag told reporters. "That has brought him to where he is now and that will bring him to being a world class player because I agree he has the potential."
"We need (exciting players) but I think every team at the top needs a player with the X factor. Garnacho definitely has it in him to become that player. If you want to be that player - world class - then you have to do it consistently and he has a high potential, 100%."
United's 19-year-old midfielder Mainoo wrapped up England's Euro 2024 campaign as a key player in former England manager Gareth Southgate's squad and Ten Hag said the experience has honed Mainoo's skills.
"Those experiences will only help him become a better player (this season). A perfect midfielder is one who is very good in attacking and very good in defending. He is a player who can do it, and he can play as an attacking midfielder and as a holding midfielder."