Ten Hag, who won the Dutch (KNVB) Cup once as a player with Twente and twice as a manager during his time at Ajax, has guided Man Utd to fourth place in the Premier League and they are still in the FA Cup, Europa League and EFL Cup.
"It's great but you play finals to win. It is not an achievement to come into a final," he told BBC Radio 5 Live: "We want to win them but first we have other things to do. We come back to the Premier League and bury this cup.
"It is good to reach the final but it is not about reaching the final, it is about winning it.
"Now the focus is on the Premier League, in two days it will continue. It has to give the motivation in the first place, we want to bring that cup to the fans.
"But in this moment I'm not looking ahead, we're focusing on other things, a big week is coming up, we have Crystal Palace and then two games against Leeds and they are going to be great games, derby games that we are looking forward to."
His words were echoed by England full-back Luke Shaw, who returned to the starting line-up after a recent illness.
"It's extremely pleasing but there's no point going to a final if we don't win it," Shaw told Sky Sports.
Ten Hag also said he couldn't think about Newcastle with six matches in the Premier League and Europa League between now and the final as his side continue their bid for a top-four spot.
However, the Dutchman has noted that Eddie Howe's side have one game a week through February and have an eight-day gap from their Premier League encounter with Liverpool at St James' Park to the final - a rematch of the 1999 FA Cup final - while United will have less than three full days from their Europa League last-32 decider with Barcelona.
"It is obvious Newcastle have an advantage but it is about attitude and mentality," he said. "I have handled it before, playing a cup game after we play in Europe, when I was with Ajax, so I know how to deal with it."
Jadon Sancho was given a rousing reception when he was introduced as a second-half substitute.
The 22-year-old has not featured since 22 October, when Ten Hag opted to give him a break from the stresses of United's first-team environment, having detected physical and mental issues he believed needed addressing.
Even after returning following a spell in the Netherlands training under the guidance of personal coaches Ten Hag knows, Sancho has had to be patient in waiting for his chance.
The enthusiastic reception he received from the United fans both before his introduction for Antony, and after the final whistle, emphasised how much they want him to do well.
A warm embrace with Nottingham Forest boss Steve Cooper, who was meeting Sancho face-to-face for the first time since their Under-17 World Cup win with England in 2017, showed the good wishes extend beyond Old Trafford.
"We speak fairly often but it was nice to see him," said Cooper.
Former United assistant-manager Rene Meulensteen told BBC Radio Five Live he feels Ten Hag was right to take his time bringing Sancho back into the fold.
"The best thing was take him out of the firing line to clear his head," he said. "I am a firm believer where the mind goes, the rest will follow.
"Now the club is more stable and his team-mates can help him. He can ease himself back, get back to his best and United fans will see what Sancho is all about."
Ten Hag added: "I thought it was great that the fans gave him love. I think he enjoyed it to be back on the pitch.
"He has been smiling in the last few weeks in Carrington. I hope he can keep this process going and of course that he has a huge contribution to the season."
Former Scotland striker James McFadden on BBC Radio 5 Live: McFadden:
I know people have said in recent years that the League Cup is not a big cup but for both teams and the progress they are trying to make, this is a massive trophy to get their hands on. It emphasises the message that both managers are trying to set out, where they want to be.
You have to start somewhere, you are not going to win league titles straight away, so they have to get that winning feeling into the players, around the club, get that feelgood factor and what better way to start.
I think the game is going to be a special game. It's two teams that want to go and play football, they have got exciting attacking players, really well balanced sides. I make it a 50/50.