"If I had played against Costa, I could never be friends, that's how it is, but when you have him in your team, it's much more fun. He is a warrior," Klopp told British media.
"What (Antonio) Conte is doing with Chelsea is outstanding but Chelsea without Costa this season?"
Costa, who won the penalty after tangling with defender Joel Matip, saw his low effort well saved by goalkeeper Simon Mignolet, which led to Klopp screaming in the fourth official's face.
"He (Costa) is not the nicest guy on the pitch but I saw no real big incident," Klopp added. "If someone tells me it was a dive, maybe I will be angry tomorrow but that would be the wrong decision what, number 27, but it doesn't make it better."
Despite the draw leaving Klopp's charges in fourth, 10 points behind Chelsea after 23 games, Liverpool did avoid a fourth successive defeat at Anfield.
"It's not been easy but we have to keep going because we cannot change the past," Matip said. "I think this was a good step to get some of this self-confidence back."
Liverpool travel to bottom-placed Hull City on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru)
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