Mohamed Salah stole the show on Merseyside with four goals and an assist as the Reds swept the Hornets aside, clinching an immediate return to winning ways following their defeat at the hands of Manchester United last weekend.
Klopp was delighted with the entire team's performance, but reserved special praise for Salah as he took his tally for the season up to 36 goals.
"It was very pleasing. It could have been really difficult tonight. We knew we had to be spot on from the first to the last second and our work rate had to be higher than 100%," Klopp told BBC Sport.
"The goals we scored were unbelievably good, and the boys didn't stop. That's how football should be, so I'm really happy with the performance. In sport, you always need to strike back against the next opponent and that's what we tried to do. We take it really seriously.
"There were a few things we needed to work on, but it was clear it was going to be a totally different game tonight. It's a big relief, I'm really happy. For Mo [Salah] to be involved in five goals is fantastic but to score four is even more fantastic.
"His goals are so important for us. We have to hope they all come back well from the internationals. The clean sheet is very important. They lost a little concentration in the last few minutes but that's normal. It helps us in the goal difference."