Wayne Rooney stepped up and duly obliged, smashing the ensuing spot-kick straight down the middle to see the spoils shared.
Liverpool stayed fourth with 30 points, 13 adrift of leaders Manchester City who were playing later at second-placed Manchester United.
The result lifted Sam Allardyce's men up to 10th, six points clear of the bottom three.
'I don't think you can disagree with the penalty - Lovren pushed Calvert-Lewin over'.
Klopp was understandably frustrated as he spoke to Sky Sports immediately after the final whistle, sharing a barbed exchange with reporter Patrick Davison.
Klopp then took a seat for his post-match press conference but he clearly hadn't calmed and carried his frustration into his meeting with the media.
"I'm quite looking forward to seeing how Everton handle them three because I wouldn't want to play against them", he concluded. "I didn't use one swearing word".
"The other team was not even in our box, I don't know if they had a shot on target apart from the penalty".
"I'd be saying: "What [are] you doing?"
Liverpool boss Jurgen Klopp must make do without left-back Alberto Moreno, who has an ankle injury.
'It's an extremely courageous decision to give that for us in a derby at Anfield and the referee got it right'. That shows how we mastered a really good side'.
Allardyce told BBC Sport: 'They've scored 12 goals in their last two games so the object of the exercise was to frustrate the opposition and I think chances created by Liverpool were minimal. But I can't honestly say they had too many clear-cut chances after that. There will be a feeling that Liverpool have no one to blame but themselves.