Klopp will be hoping to land his first piece of silverware for the Merseysiders on Sunday when he leads out his side to face Manchester City in the League Cup final at Wembley.
Mignolet had been at fault earlier when City took the lead in the 49th minute, when he failed to deal with a shot by Fernandinho.
“He is now a Manchester City player and he will try to win for us”.
Mignolet and Caballero made vital saves in extra time but City clinched the season’s first trophy in dramatic fashion to give Pellegrini his second League Cup, having also lifted it two years ago as well as the Premier League title.
Klopp has now lost his last four finals as a manager.
“My first game with the club [was at Wembley] and unfortunately we couldn’t play well enough”.
So, for the third year in a row, the game went to extra time and Aguero again came within inches of scoring but was again denied by a great save from Mignolet.
A visibly angry Sakho was replaced soon after by Kolo Toure because of possible concussion following a clash of heads earlier in the 16th minute with Emre Can that saw both players needing attention.
It then could have been game over for Liverpool as they survived to major scares in quick succession.
Two City old boys nearly combined to forge an equaliser, James Milner shooting wide from Daniel Sturridge’s through-ball, before Raheem Sterling – roundly booed by fans of his former club – squandered a gilt-edged chance to make it 2-0 by shooting wide from David Silva’s pass.
Moments later City should have had a penalty when Moreno brought down Aguero in the area with a clumsy challenge but referee Michael Oliver inexplicably said no and allowed Liverpool to clear.
Pellegrini’s men continued to make all the running and Klopp threw on Lallana and Divock Origi as his team appeared to be slipping towards defeat.
Captain Vincent Kompany also praised Caballero, describing him as the hero of the day ahead of the final penalty taker Yaya Toure, who made no mistake from the spot.
Coutinho equalized for Liverpool in the 83rd minute from close range after an Adam Lallana effort hit the post and rebounded neatly into the path of the Brazilian midfielder.
Meanwhile, rising Manchester City star Kelechi Iheanacho is determined to repay Manuel Pellegrini for giving him his chance this season. Please note that comments are automatically checked for inappropriate language and will be removed accordingly.