Klopp believes his men deserved to beat Sean Dyche’s side after putting up a ‘top performance’ at the Turf Moor.
The hosts were determined to keep Liverpool at bay but the Reds found their breakthrough on the cusp of halftime through Roberto Firmino’s sixth away goal of the season.
Defender Nathaniel Phillips got Liverpool’s second of the night just seven minutes after the break before substitute Alex Oxlade-Chamberlain sealed Klopp’s side’s victory during the dying embers.
"It was a semi-final. We had to win the semi-final and we did. Nothing is decided yet but we improved our position and we have the final. That's what we needed. It's what we deserve because this was a top performance,” Klopp said after the game.
"You can't give any chance away against Burnley because of the way they play. They wanted to go for our centre-halves but our boys did outstandingly well.
"We knew before the game it would be incredibly tough - we had about 3,500 people not on our side. Atmosphere in football is massive.
"I thought the boys deal really well with that. They didn't get distracted - they tried to use it because noise is nice. We played a lot of good football stuff."
He added: "We saw it as a semi-final. You can't go to Burnley and hope to win 3-0. It's usually incredibly tight.
"We have to make sure we recover quickly. We have a thin squad in some positions. We have to wrap them in cotton wool. I can't wait for the 10,00 fans at Anfield. Nothing is decided - Palace are strong."
