The former Ajax manager was in the stands at Selhurst Park to watch his new side go down 1-0 to Crystal Palace on the final day of the Premier League season - Ralf Rangnick's final game as interim head coach.
However, West Ham United's loss away to Brighton & Hove Albion means that the Red Devils still secured sixth place and a spot in the Europa League for the 2022-23 season.
Ten Hag takes over on a three-year deal from Rangnick, who has moved into a consultancy role alongside his Austria duties, and the Dutchman is aware of the size of the task awaiting him at the club.
"The current situation is obviously not that good. It's a big challenge. I want to build and construct a team who are battling for each other, who are unified and who will get results. Also we are playing in the Theatre of Dreams," Ten Hag told MUTV.
"We want to entertain. But in the end, the intention is to play fantastic football. If we can't play fantastic football, we still have to win."
Ten Hag is reportedly planning a boot camp after being left concerned by the fitness standards of Man United's crop, and the 52-year-old expects his side to engage in "total high-pressing" under his tutelage.
"The way we did it - with dominant, dictating football - that is the way I want to act in Man United as well. "But finally the competence and the quality of the people - so the players - decide how you have to play," Ten Hag added.
"We are playing in the Theatre of Dreams and have to entertain the opponent. We are playing in the opponent's half and we have to do attacking football. We have to do the pressing, the total high-pressing - that is a similarity also - and the adventurous football."
Ten Hag also revealed that he hopes to take inspiration from the Sir Alex Ferguson days of Man United, and he is keen to bring that "identity" back to the Theatre of Dreams during their push for honours.
"It's about the Man United football and about the Man United identity and philosophy. I think that you pointed it out: it has to be about attacking football," Ten Hag explained.
"We have to bring structures in the way of playing, so we can play attacking football. Of course. I know the history of Man United, I know the big times and the audience, the vibe that can be around Old Trafford.
"I watched them in their big times, when Sir Alex Ferguson was manager, during the really successful times when they won titles and were dominating Europe.
"But also before Sir Alex, Man United was a really big club and I know names like [Matt] Busby and [Bobby] Charlton that gave Man United a presence to the outside world from winning, and winning in a spectacular way, winning so they entertain people. What stays with me is there was always a fighting culture. They fight together and they get success."
Ten Hag left Ajax having won 159 of his 215 matches in charge of the club, picking up three Eredivisie titles and two KNVB-Beker crowns in that time.