Hojlund, 20, has joined Manchester United in a move worth up to £72 million ($91 million). Kane, who was heavily connected with United throughout their quest for a striker, is set to join Bayern Munich for more than £100 million.
"We have chosen a striker, and we are very pleased with our choice," Ten Hag said at a news conference on Friday.
"[Kane] is a great striker, a goal maker, and he has all the characteristics and abilities that you want to see in a striker." Definitely a miss for the Premier League."
Kane, 30, has been a Premier League mainstay for nearly a decade and scored 30 league goals last season.
Meanwhile, Hojlund remains unproven at the top level, scoring nine goals for Atalanta in Serie A last season.
Ten Hag declined to explain why Hojlund was chosen over England captain Chris Smalling ahead of United's Premier League opener against Wolverhampton Wanderers on Monday.
"I don't think I have to get into that debate or express an opinion on it," he said.
"We are professional, and we take great care in our processes." We think about a lot of factors before making a decision, but it doesn't happen overnight. We carefully consider every decision, and we are pleased with the team we have assembled."
Hojlund will miss the game against Wolves due to a back ailment, but Ten Hag dismissed concerns that the Denmark international could be out for a lengthy time.
"As we previously stated, he had a minor issue," Ten Hag explained.
"He's not at the level of our players right now, so we have to train him." The prognosis is always tough to predict. We are confident and optimistic."
Meanwhile, Ten Hag has stated that Harry Maguire is still eligible to play against Wolves on Monday, despite West Ham boss David Moyes revealing that a £30 million bid for the England defender has been approved.
"We've had a bid accepted from Manchester United, but I'm not in a position to discuss him because he's not our player," Moyes added.

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