Trent Alexander-Arnold struck late on to win the game 2-1 in the Reds' favour.
Klopp later said: "We dominated the game but we made one mistake and concede a goal. Then we score the equaliser but it's ruled out for offside. At half-time it wasn't the best mood, you can imagine but the words were OK. I didn't have to lift them too much, they knew if we continue to play like we did we would create chances again. We dealt with their game really good. It was massive, it felt massive to win. A real relief.
"We were there, we defended well, we were constantly in the creating mood without having 20 clear-cut chances. We needed that win today, these three points feel big.
"We can stop that chat about Trent, everyone agrees that he is an outstanding player. It's Gareth Southgate's decision what he does for the squad but we don't have to talk about it every week. We don't have to justify the players' status every week.
"We have to put the other teams under pressure. Everyone knows that when we get on a run we are dangerous."