Zirkzee, signed by United from Bologna last month, came off the bench to score their lone goal in a 1-0 win over Fulham in United's Premier League opener last Friday, displaying the nimble dribbling skills that the 6-foot-4 Dutchman is known for.
"Very pleasing that a player who is a striker scores his first goal in his first game," Ten Hag told reporters on Thursday. "That will give him confidence, we're very pleased that it's happened.
"I give the comparison last year with Rasmus Hojlund that when he scored against Brighton and the VAR looked, five minutes later they came to the conclusion the ball crossed the line in the assist and he had to wait three months for his first Premier League goal," Ten Hag added.
"It helps absolutely (Zirkzee) scoring his first goal, it gives him confidence and gives us confidence as a team. Very good progress."
Hojlund, who scored 10 league goals last season, remains sidelined this week with a hamstring injury, along with Luke Shaw, Tyrell Malacia and Victor Lindelof.
"(Lindelof) has an issue on his toe, hopefully he can return quickly but not available for the weekend," Ten Hag said.
The manager was non-committal on the status of Jadon Sancho, who returned to United last month after a very public spat with Ten Hag last year which led to him finishing the 2023/2024 season with Borussia Dortmund. Sancho did not feature in Ten Hag's squad against Fulham.
"We will see. You need them all (the players) throughout the season because it is survival of the fittest," Ten Hag said.
"We have to manage it, the attitude of the players is very important, sometimes they will be disappointed they are not in the starting XI but they have to deal with it, you win as a squad.
"The prizes are decided next May and until then we need all the players in the squad and highly motivated, that is not an expectation, that is a demand on the squad. The team is always more important than any individual."
