Antony only completed his big money move to Old Trafford on transfer deadline day on Thursday but was thrust straight into the starting eleven against Mikel Arteta's table-topping side.
It took the 22-year-old just 35 minutes to score his first goal for his new club, becoming the ninth Brazilian player to play for Manchester United in the top flight and the first to find the net on his debut.
Antony was withdrawn on the hour mark for Cristiano Ronaldo but Ten Hag expects a player he coached at former club Ajax to improve further as the season progresses.
"I think we've all seen what a threat Antony is. His speed and creativity can be a real threat in the Premier League," Ten Hag told Sky Sports.
"We missed a player on the right wing, because all the players who can play there, like Jadon Sancho, like Marcus Rashford, they prefer more the centre or the left side.
"Now we have the one who can play really well over on the right wing. That was a missing link. Today, his first performance here, he did well but I think he can step up.
"I know him from Amsterdam and I know this is a different league, but there is potential and he will be even more of a threat to opponents than he was today."
Manchester United have now won four games on the bounce after losing their first two matches.
