Sadio Mane scored twice, while goals from Philippe Coutinho, Emre Can, Roberto Firmino and Georginio Wijnaldum crowned the club's eight league win of the campaign.
Daryl Janmaat struck a consolation mid-way through the second half for a Watford side who missed the chance to surge into the top six.
The Hornets remain under investigation over allegations they forged bank letters, and their off-the-field problems finally caught up with them as their four-match unbeaten run came to an end.
Despite taking their goal tally for the season in the top flight to 30, Liverpool are now without a clean sheet in their last four games after Janmaat took advantage of some slack defending to slide past Loris Karius. Klopp was left disappointed by the goal, which overshadowed an otherwise impressive display.
"At some specific moments I enjoyed it a lot but there were some other moments when I did not enjoy, and it was harder work when in the end it looked like it wasn't," the Liverpool boss told Sky Sports. "It was a brilliant performance over 84 minutes, for six mine we were not that good.
"Not because we conceded the goal; they were really concentrated and really tried to do the right thing in the right moment and there was a lot to do in the end. We conceded the goal at the end which isn't too nice but that is normal. We are not used to being that successful so in the moments we were not serious. We played too quickly and gave them the opportunity to win easy balls.
"Only one goal we conceded but the problem is we have to run so it costs us energy for the other situations. There are a lot of things that we can improve on, that's good. Everyone who saw the game will have enjoyed it so it was quite a nice performance."
Illness threatened to disrupt Liverpool's preparations during the week, as a fever spread through the squad in the lead-up to the game. James Milner missed the win at Crystal Palace through feeling unwell but did return to the team, while Can and Wijnaldum were both absent from training.
But Dejan Lovren was forced out of the starting 11 and replaced by Lucas Leiva, and Klopp has revealed how the bug almost unraveled the club's plans.
"We had a lot of problems during the week," he added. "A lot of players were ill for one day, two days and came back. That was not enough for Dejan, he is now ill; bad timing."