The Reds won 6-5 on penalties after a goalless 90 minutes and extra time, repeating their shootout victory over Chelsea in the Carabao Cup final.
“I couldn’t be more proud of my boys, the shift they put in, how hard they fought,” Klopp said, speaking to BBC Sport.
“It was an incredible game, a nerve-wracking shootout, my nails are gone.”
Klopp, 54, became the first German manager to win the FA Cup after defeating compatriot Thomas Tuchel in a second Wembley final in less than three months.
The shootout went to sudden death, as in the February final, with Alisson’s save from Mason Mount giving Liverpool the advantage before Konstantinos Tsimikas tapped home the winning penalty.
“It was intense – Chelsea would have deserved it exactly the same way we did, just like in the Carabao Cup – that’s how small the margins are,” Klopp added. “Chelsea played outstanding but in the end there must be one winner and that was us today.”
The thrilling win kept Liverpool’s faint quadruple ambitions alive – albeit the Premier League title may yet elude them – with two games remaining, they trail leaders Manchester City by three points and have a goal differential that is seven points worse.
“The quadruple thing is absolutely outstanding that we can talk about it. It’s crazy,” the Red-team coach said. “It’s out of this world – this was game number 60 in an intense season.”
Klopp famously dubbed his team “mentality monsters” for how they have responded to setbacks this season as they chase greatness on four fronts.
However, the Reds manager stated that Tuchel’s Chelsea deserved the title as well after their contribution to another exciting match between the two clubs.
During a tense spell of normal time, both teams had gilt-edged chances, with Luis Diaz and Andy Robertson for Liverpool and Marcos Alonso for Chelsea hitting the crossbar.
“I really feel for Chelsea – for the second time, 120 minutes and you get nothing, that’s too hard. But for us I’m pretty happy,” Klopp said. “We are mentality monsters but there were mentality monsters in blue as well – it was one penalty that was the difference.”