In Wednesday's game, the Merseyside club took the lead twice within 20 minutes thanks to two goals by Roberto Firmino but were pegged back after Mignolet was easily beaten by Aaron Ramsey at his near post and then by Olivier Giroud from a corner.
However, with British media reporting that Mignolet is set to sign a new five-year contract, Klopp said the goalkeeper was not the only one to blame for the blunders.
"For the second goal he needs help from all the players," Klopp told reporters after the game.
"On the second goal, on a perfect day he can make a save but there were a lot of mistakes before. We have to defend this better."
With Mignolet struggling and his deputy, Adam Bogdan, making numerous mistakes in his rare outings, Liverpool recalled goalkeeper Danny Ward from his loan spell with Aberdeen on Monday.
Liverpool dropped down to ninth place in the table and host Manchester United, in sixth, in the league on Sunday.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Pritha Sarkar)
