The Dutchman has now officially started his reign as manager of the 20-time English champions, who finished the 2021-22 Premier League season down in sixth spot in the table.
Ten Hag was in attendance for Sunday's 1-0 loss at Crystal Palace, with the result still proving enough to claim a Europa League spot for next term, as seventh-place West Ham United lost at Brighton & Hove Albion.
The former Ajax head coach is confident that the Red Devils will be able to take on both Manchester City and Liverpool during his time at the helm.
"In this moment I admire them [Pep Guardiola and Jurgen Klopp]. I admire them both. They play, in this moment, really fantastic football – both Liverpool and Manchester City," Ten Hag told reporters on Monday.
"But you will always see that an era can come to an end. I am looking forward to battling with them and I am sure all the other clubs in the Premier League will want to do that."
However, the Dutchman has accepted that it will take time to help the club return to the top of English football, so a top-four finish in next season's Premier League is the main target.
"I said this is the project, to bring Man United back on top, but also we have to accept the current situation we are in," Ten Hag told MUTV. "First of all, Man United belong in the Champions League, so that will be the first target."
Man United were still in the top-four race in the Premier League heading towards the latter stages of the season, but their disappointing form allowed both Arsenal and Tottenham Hotspur to pull clear, with the latter ultimately claiming fourth spot in the table ahead of their North London rivals.
The 20-time English champions finished 35 points behind champions Man City, 34 behind second-place Liverpool and 13 behind Spurs, who showed impressive form in the latter stages of the campaign under Antonio Conte, who was linked with the job at Old Trafford during a difficult period for Ole Gunnar Solskjaer.
Man United also struggled in the two main cup competitions in England during the 2021-22 campaign, exiting the FA Cup in the fourth round and EFL Cup in the third round.
Ten Hag led Ajax to two Dutch Cups during his time in Amsterdam, and the incoming head coach has also detailed the importance of the other competitions aside from the Premier League.
"For me, every game is important," he told MUTV. "We want to win every game and that has to be the attitude from everyone: players, but also staff and all the other ones in the club.
"Every game is important and we will give our best in every game to win and to come forward."
Ten Hag also confirmed on Monday that the team would begin their pre-season preparations on June 27, although those involved for their countries will receive more time off.
"We will start pre-season on 27 June and I will get a few of the squad, of the individual players. Not all the players will be coming in [on 27 June], because the ones who play internationals will have a longer break, because they play longer in this current season," the Dutchman added.
Ralf Rangnick has stepped aside at Old Trafford to allow Ten Hag to take control of the team, but the German, who led the Red Devils on an interim basis following Solskjaer's departure, is set to take on a consultancy role at the club.