The English goalkeeper kept the Reds at bay with some exquisite saves as Burnley snatched a 1-1 draw against the newly-crowned Premier League champions.
Pope made a super stop to deny Mohamed Salah early on and then brilliantly denied Sadio Mane late on the cusp of halftime.
In an interview with BBC Sports after the game, Klopp said it was his side against Pope and admitted Liverpool should have converted their chances.
"For moments it was Liverpool against Pope, he did really well, but we should have scored,” the former Borussia Dortmund boss said.
“We did everything right and he made saves but we should have scored more, that's on us.”
"We didn't close the game and they took their moment. It feels like we lost a game, we have to look after the game better.”
“We were angry with the referee but we have to criticise ourselves first for not finishing the game.”
"The team do it right 99% of the time but I will never stop criticising them."
Next up for Liverpool is a game versus Arsenal at the Emirates Stadium on Wednesday before a penultimate fixture of the season against familiar foes Chelsea at Anfield.
