Emre Can's stupendous mid-air scissors kick earned Liverpool a 1-0 win at Vicarage Road on Monday that provisionally gave them a three-point cushion over Manchester City in third place.
Victory in Liverpool's last three games – against Southampton, West Ham United and Middlesbrough – will guarantee them a Champions League berth, but Klopp said there was still much work to be done.
"We need to stay focused, we need to stay concentrated," said the German.
"We have pressure until the end of the season, but that's a positive pressure. It means we are fighting for something.
"So we'll do everything for the points we can get, but it won't be easy.
"If people think we already have the three points against Southampton then they've not seen them play this season. Another really strong side.
"Nobody can take these points away from us tonight and now we have time to work and prepare for the Southampton game (on Sunday)."
Can settled proceedings in first-half stoppage time, meeting Lucas Leiva's floated pass with a picture-book volley that flew past Watford goalkeeper Heurelho Gomes.
Can has battled a niggling calf problem for the past 12 months and Klopp praised the Germany midfielder for gritting his teeth and fighting through it.
"If he couldn't be positive after this goal, something would be wrong," Klopp said with a smile.
"He's a good player. He'd had a calf problem, but we couldn't leave him out. We had a lot of talks about this.
"People wondered what was wrong with him, but we needed him in these moments. He said, 'I'm going to try.'
"Sometimes he wasn't as good as he could have been, but now those problems are sorted, he's physically strong and he can build on these performances.
"And if he can score goals like this it makes even more sense."
Mazzarri bemoans bad luck
Liverpool lost playmaker Philippe Coutinho to a dead leg early in the game, which saw Adam Lallana make his return from a month-long lay-off as a 13th-minute replacement for the Brazilian.
Klopp offered no prognosis on Coutinho's condition, only to say that the injury – sustained in a collision with Watford's Adrian Mariappa – had been "really painful".
Liverpool also hit the bar through a dipping Lallana volley and Watford goalkeeper Heurelho Gomes had to make several second-half saves to keep them at bay.
But the hosts came within millimetres of snatching a stoppage-time equaliser when centre-back Sebastian Prodl thundered an effort against the crossbar.
"I said to the players after the game, if they want to kill me, that's a good way to try it. I thought I felt something in this area," Klopp said, gesturing to his heart.