Teenager Garnacho silenced a fired-up Goodison Park after just three minutes with an overhead finish that will be a contender for goal of the season.
Former United stars Rooney and Ronaldo both struck similar goals during their stellar careers, but Ten Hag insisted it was too soon to bracket the 19-year-old Garnacho in such vaunted company.
Ten Hag, who saw his side seal maximum Premier League points with second-half efforts from Marcus Rashford and Anthony Martial, said: “Don’t compare, I don’t think it is right.
“They all have their own identity, but for Garnacho to go that way he has a lot to come, he has to work very hard.
“You have to do it on a consistent basis and so far he has not, but he definitely has high potential to do some amazing things.
“It’s not the first time we saw this, we have already often seen glimpses, but if you want to be a player like Rooney or Ronaldo you have to score 20-25 goals in the Premier League each season.
“That’s not easy to get, you have to work hard, you have to go in areas where it hurts. So there’s a lot to come. But potential, he has.”
Ten Hag, whose side made it five wins from six top-flight matches to close the gap at the top of the table to six points, felt Garnacho’s opening goal was extra special because of United’s build-up.
The former Ajax manager added: “It was fantastic goal and this season there’s still many games to play, but probably already maybe the goal of the season.
“But not only the finish, it was the total from the back to the end, but of course the finish is incredible.”
Goodison Park was a cauldron before kick-off as Everton fans launched their protest at a 10-point Premier League deduction, with marches prior to the game and most fans in the stadium waving mini purple ‘Corrupt’ placards.
Everton responded well to Garnacho’s opener, creating several clear-cut chances before being punished after the interval for not taking their chances.
Manager Sean Dyche said it was difficult to criticise his players after his side slipped five points from safety in their first game since being handed the punishment for breaching the league’s profitability and sustainability rules.
Dyche said: “It’s a tough one to call, for a large part we were very good, particularly the first half.
“They get off to a worldie, a lifetime goal and got the better of the first 15 minutes, but then we regrouped well.
“They ended up kicking it long. We created chances but couldn’t end up scoring a goal and it hurts you in the end.”
Rashford converted United’s second from the penalty spot after a VAR intervention before Martial’s neat late finish, while Everton struck the woodwork through Vitaliy Mykolenko’s second-half shot.
Dyche added: “It is very difficult when the second and third go in. We hit the bar, the biggest thing for me is the chance count, incredibly high again.
“But we have to be clinical. I think a lot of the performance was right, the fans were terrific.
“They were having their own say and that connection with the fans is going to be important.”