Garnacho scored with a stunning overhead kick in the third minute to fire United to a 3-0 victory over Everton at Goodison Park, leaping to meet Diogo Dalot's cross with an acrobatic scissor kick into the top right corner that instantly drew comparisons with former United striker Rooney.
"The season, still many games to play, but probably already the goal of the season," Ten Hag told reporters.
"It was incredible."
The Argentinian teen said he himself couldn't believe he had scored.
"I didn't see how I scored, I just listened to the crowd and said 'Oh my god,'" Garnacho told NBC.
"One of the best goals I've scored, I'm very happy."
The strike echoed goals by Rooney and fellow former United striker Cristiano Ronaldo, particularly Rooney's bicycle-kick stunner during the 2011 Manchester derby.
"I can't believe it," former United captain Gary Neville said on the Sky Sports broadcast.
"I don't think I've ever been in a stadium where I've seen an overhead kick as good as that - and I was there on the day that Rooney scored his in the Manchester Derby."
Ten Hag, however, was uncomfortable comparing Garnacho so quickly with two of the club's biggest names of recent years.
"Don't compare," said the manager, who served a one-game suspension on Sunday and so was not on the touchline.
"I don't think it's right. They all have their own identity, but for Garnacho to go that way, he has to work very hard. And you have to do it on a consistent basis. And so far, he's not.
"But he has definitely high potential to do some amazing things. It is not the first time we saw this.
"But if you want to be a player like Rooney or Ronaldo, you have to score 20, 25 goals in the Premier League and that's not easy to get. But potential, he has."
The goal silenced the Goodison Park crowd except for the travelling United supporters who loudly sang "Viva Garnacho."
Even Everton manager Sean Dyche marvelled at what he called a "lifetime goal."
