Lovren was penalised for a push on Dominic Calvert-Lewin late in the second half, with Wayne Rooney converting from the spot to level the scores after Mohamed Salah had put the Reds in front in the first half.
The home side enjoyed nearly 80% of the ball but could not make the most of their dominance, and Klopp could not hide his frustration at two more dropped points during his post-match media duties.
In a testy exchange with a Sky Sports reporter, Klopp insisted that Lovren's challenge did not warrant a penalty and criticised Everton's tactics of defending deep inside their own half.
"I saw only one team playing today," the German said. "With all the challenges in this game, and only one team playing, to give such a penalty away is unbelievable."
Klopp then asked the interviewer for his view on the penalty and when the reporter replied that he thought it was the right decision, he shot back: "Then we can stop the interview, because I only want to talk to people who have a little bit of an understanding of football."
Eyebrows were raised in the lead up to kick-off at Anfield after it was announced that Brazilian duo Philippe Coutinho and Roberto Firmino would both be starting on the bench for the hosts, with Klopp making six changes to the team that thrashed Spartak Moscow in the Champions League.
"I make decisions before I know they are right, and afterwards it is your job to say I'm not right," the Reds manager said when questioned about his team selection.
"Yes I was sure this was the right decision, we brought Roberto Firmino on for Mo Salah, so, we could have scored before, we could have scored afterwards.
"We lived more or less in their box. But obviously we didn't do it, I have to take that."