Ten Hag steered United to the trophy during his first season at Old Trafford in 2022/23 before adding the FA Cup last term, defeating Manchester City in the final following a disappointing campaign in the Premier League where United finished eighth - a mammoth 31 points adrift of local rivals and champions City.
Many leading English clubs have come to regard the League Cup as an inconvenience that hampers their quest for more prestigious domestic and European honours.
United face third-tier Barnsley in the third round of the League Cup on Tuesday and Ten Hag was asked during a pre-match press conference if the club now needed to win something more significant now their football operations were under the control of British billionaire part-owner Jim Ratcliffe's Ineos group.
"I would say it's significant," said Ten Hag. "FA Cup, Carabao (League) Cup, it's significant. I see all the attention from all the teams, from all the owners, from all the managers when they win a trophy, like Liverpool last year did, winning the Carabao Cup.
"I saw that final. I saw all the teams battling for it. We want the same. So it's very important in football to win trophies. You have five opportunities, and our aim is always to win all the games, so win all the trophies if possible."
'Take it seriously'
The Dutchman added: "No doubt we are aiming for a trophy, this is one opportunity, so we take it (Tuesday's game at home to Barnsley) seriously."
United are currently 10th in the early season Premier League table with six points from four matches.
They bounced back from consecutive losses at Brighton (2-1) and at home to Liverpool (3-0) to win 3-0 at Southampton on Saturday.
Lisandro Martinez and Noussair Mazraoui, however, both limped off in the second half of that success on the south coast, with their fellow defender Matthijs de Ligt also withdrawn because of cramp.
Nevertheless, the trio are all fit to be selected for Tuesday, with Ten Hag saying: "They are all available, they are good."
But the United boss added Rasmus Hojlund, Mason Mount and Victor Lindelof will not return against Barnsley as they continue their respective recoveries from injury, although he refused to rule them out of Saturday's league match away to Crystal Palace.
Ten said Luke Shaw would not be involved in the League Cup tie, although he was upbeat about the England left-back's rehabilitation following a calf problem, saying: "He is progressing well.
"Of course we have a plan in our head when he can be ready. But you're always dependent on how the progress will go and you can't make a suggestion, because there are so many factors why a rehab plan can accelerate or slow down."
Mazraoui and De Ligt's fellow pre-seaon signing Manuel Ugarte could make his first United start after the midfielder came off the bench for his United debut on Saturday.
But Ten Hag was coy when asked about the possibility that Antony, who has made just one appearance as a late substitute at Brighton so far this season, starting against Barnsley.
"You will see what the line-up will be (on Tuesday)," he replied. "We have every day training and the players have to earn the right to play."