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Mignolet struggled as the Reds twice gave away the lead in a thrilling 3-3 draw with the Premier League leaders.
"For the second goal he needs help from all the players," said Klopp, in reference to Mignolet scrambling as Olivier Giroud scored from a corner.
The Belgium goalkeeper, 27, is set to sign a new five-year contract.
Mignolet, who joined the Reds from Sunderland in a £9m deal in June 2013, was also beaten at his near post by Aaron Ramsey for Arsenal's first equaliser.
Klopp, who has consistently backed Mignolet, added: "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."
Liverpool's goalkeeping weaknesses have been exposed by errors from Mignolet's deputy Adam Bogdan in the 3-0 defeat at Watford and the 2-2 FA Cup draw at Exeter.
That has prompted Klopp to recall 22-year-old Welshman Danny Ward, a substitute on Wednesday, from a successful loan spell at Aberdeen.
Liverpool snatched a deserved draw with Arsenal thanks to Joe Allen's late equaliser.
Roberto Firmino twice gave Liverpool the lead in a breathless first half, the second a spectacular 20-yard drive, but Arsenal levelled through Ramsey and Giroud.
Giroud's second-half strike - his 18th goal of the season - looked to have put the Gunners on course for a crucial victory, but substitute Allen rewarded the hosts for a display bursting with energy and spirit with a low 90th-minute finish.
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Klopp was delighted with the performance of Brazil forward Firmino, who has struggled to live up to his £29m transfer fee since arriving from Hoffenheim in the summer.
The German said: "I could talk about this for half an hour. He doesn't know how good he is. If you are good, you have to show it.
"He had a really good game but he was not the only one. I could talk about special performances - we had a lot of other players."
Klopp was also involved in an angry first-half exchange with fourth official Robert Madley and was calmed down, amiably, by his opposite number Arsene Wenger.
He said: "I told Arsene why I was a little bit emotional. It was a clear throw-in for us in a good moment, a good phase. I said what I said, he said what he said.
"We had nothing, it was friendly."
Liverpool boss Jurgen Klopp defended under-fire goalkeeper Simon Mignolet after his latest uncertain display in the draw with Arsenal at Anfield.