The game went to penalties after Takumi Minamino's last-gasp goal in stoppage time levelled the affair at three goals apiece in an instant classic at Anfield.
"I am really, really happy. Really happy with the performance, with the spirit, with the mentality, in a lot of moments with the football," Liverpool boss Jurgen Klopp said.
Jota gave Liverpool some life in the 68th minute with a goal in front of the Kop, but it was Minamino's goal in the waning seconds that sent the game to penalties.
Minamino then spurned a chance to send Liverpool through in the ensuing shoot-out as he blazed his effort over the bar. But Kelleher then saved Ryan Bertrand's effort, his second save of the shoot-out, before Jota converted.
Klopp added that he gladly give up home advantage to also see Liverpool not have to play two games for the semifinals in the first two weeks of 2022 given the lack of winter break and packed festive program stretching the squad.
"The draw has us at Arsenal, I'm fine with that, we play there and see who is better and go for it," Klopp said. "I don't just speak about player welfare this year, I have been speaking about it for six years or maybe longer.
"If the things I say would help more, I would say it much more often. But it doesn't help. The only thing I do with these messages is I create headlines. They never arrive at the right places."