Karius endured a torrid evening in Kiev, as he made two massive errors directly leading to goals in Real Madrid's 3-1 win.
Liverpool landed Alisson from Roma earlier this month, splashing out a world-record £65 million (€73m/$85m) fee for a goalkeeper.
And Klopp denied that Karius' performance in Kiev caused him to go in search of a new goalkeeper.
"If we had won the final and Alisson had been on the market we would have gone for him because we think he is the goalkeeper we want,” Klopp said.
“The other goalkeepers are really good, like our midfielders. It doesn't mean we tell Fabinho: 'Sorry, we already have good players we don't need you'.
“We bring in another one because we think we can make the next step like with Naby [Keita]. We do it and it's the job.”
The German boss also said that he had not discussed Alisson's arrival with Karius prior to the transfer.
"Listen, I didn’t walk through the dressing room and tell people that I was signing Fabinho or Naby Keita,” Klopp said.
“I didn’t say before the medical, 'we are signing a goalkeeper' and then it’s like, 'oh!'"
Klopp also spoke out for the first time on Sergio Ramos' challenge on Mohamed Salah in the Champions League final, calling it "ruthless and brutal."