The Dutch coach became the first United manager to lose his opening two games in charge for more than a century as defeats to Brighton and Brentford left the Red Devils bottom of the Premier League for the first time in 30 years.
On a big night for Ten Hag, his decision to drop Cristiano Ronaldo and club captain Harry Maguire paid dividends as United's high tempo blitzed Liverpool for the opening 30 minutes.
Jadon Sancho gave the home side a deserved halftime lead before Marcus Rashford's first goal since January put United 2-0 up.
Mohamed Salah pulled a goal back for Liverpool 10 minutes from time, but Jurgen Klopp's men have now failed to win any of their first three league games of the season to fall seven points behind leaders Arsenal.
"We can talk about tactics but it is all about attitude," said Ten Hag.
"I am happy with the performance but we have to bring it every game. Don't just bring it against Liverpool. Every Premier League game is difficult, we need to bring it to every game. It starts, once again, with the spirit."
Ten Hag reportedly dragged his players in on a planned day off to run 13.8 kilometres the day after a 4-0 defeat to Brentford last weekend.
That was the extra distance covered by Brentford players and United collectively covered 18 kilometres more than eight days ago with a number of players struggling with cramps in the closing stages.
"Today was really important for us," said Bruno Fernandes, who was made captain in the absence of Maguire.
"We showed the right intensity and more importantly the right character. We got the three points. Scoring first was really important for us, for our confidence.
"It was important for us to take the first step in the league, now we have to carry on"
Victory took United above Liverpool in the league table and to within four points of the top four.
Casemiro was paraded at Old Trafford before kick-off, but United's latest £60-million signing had to settle for a seat in the stands as the Brazil midfielder was not registered in time to make his debut.
Ten Hag hinted that more money will be spent in the final 10 days of the transfer window, but said there was also a route back into the team for Maguire and Ronaldo.
"I don't have to mention Maguire and Ronaldo. They are amazing players and they will play a role in the future and the short-term future as well," he said.
"We have the right players, I am convinced of that. The window is not closed and you need numbers and also quality."