Watford, led by new boss Nigel Pearson, defended deep and frustrated Liverpool whilst creating some clear-cut chances for themselves in the first half.
Nevertheless, Liverpool survived the scares and went ahead in the 38th minute as Mohamed Salah finished excellently with his right-foot to round off a quick Liverpool counter-attack.
The Anfield crowd showed signs of anxiousness, which translated to the players on the pitch as Virgil van Dijk nearly netted in his own goal before Watford had another few chances to take something from the game.
However, Liverpool rode their luck and sealed victory in the final minute to as Salah produced a stunning back-heel flick from close-range to roll the ball past goalkeeper Ben Foster.
When questioned whether Liverpool needed to dig deep, Klopp said: "Yes, that’s how it is. At 1-0, that’s the result you never can rely on that the game is decided. No problem with that.
"In December and January especially, you need to show resilience – that’s the most important thing. And we showed that, but Watford showed it as well, so I respect that.
"We had chances, we scored goals, but they had chances as well which they didn’t score from – and that’s for sure one reason why they are in the situation they are in. Two or three balls they missed.
"This time maybe now I can speak about, but the wind helped us today from time to time – I am pretty sure Sarr would have at least had a finish in the situation when he didn’t hit the ball without the wind.
"It made the game tricky for both sides, that’s clear, but it helps them a little bit more than us usually in those situations.
"Ali was for 85 minutes of the game really doing warm-up exercises, but in these [other] five minutes he was really important and just showed what a goalie he is; he is unbelievable and helped us a lot in these situations.
"We had to fight, that’s what we did and that’s why we won. All good."
The boss also provided an update on Gini Wijnaldum, who was forced off in the second-half due to a knock, revealing the Dutchman will miss Liverpool's trip to Qatar for the Club World Cup later this week.
Liverpool's win over Watford means the Reds have now earned 49 points from a possible 51 in the league this season - an unprecedented run which puts them in the driving seat for the Premier League title.