The Reds had dominated the Merseyside derby from the outset and took a deserved lead three minutes before the break through Mohamed Salah's 13th Premier League goal of the season.
Liverpool squandered a number of good opportunities in the second period and were made to pay for their profligacy when Wayne Rooney lashed home from the spot after Dejan Lovren bundled Dominic Calvert-Lewin over in the area.
Klopp was in a combative mood after the match, taking aim at the referee and what he considered to be a negative and overly aggressive approach from Sam Allardyce's side.
"Lovren doesn't make a challenge," he fired at Sky Sports when it was suggested that the penalty decision was correct. "Calvert-Lewin makes a step. The hand is on the back. If you think it is a penalty say so. Does my opinion change anything?
"I only want to speak to people with a little bit of understanding about football. I am sorry, I am wrong and you are right. Obviously I am not in the mood to answer questions.
"Our performance was good. I saw only one team playing. I can't believe the situation with all the challenges. We were clean and didn't make any fouls.
"There is always one nasty one – [Gylfi] Sigurdsson made that. A clear red card. You see the picture of the penalty. Calvert-Lewin is smart but it is nothing. But it is a penalty and one team can celebrate and we can't.
"I don't understand why the ref is doing that [giving the penalty]. I didn't use one swear word. Only one team is trying over 95 minutes to win it. The other team are not in our box and didn't have a shot on target bar the penalty."
Klopp had earlier made the surprise decision to name Philippe Coutinho and Roberto Firmino on the substitutes' bench and then took Salah off with more than 20 minutes remaining.
The bullish German added: "That is my job. I make decisions that I think are right. It is your job to say afterwards if it is right.
"We lived more or less in their box. We could have scored earlier. I have to live with that."