Klopp was visibly furious after Liverpool conceded an equaliser from the penalty spot late on in Sunday's Merseyside derby.
When Davison provided his view that while the decision was soft, the penalty call was warranted, Klopp dismissed the interviewer's credentials.
"Calvert-Lewin makes it smart, but he makes a step in this direction and even then it's nothing".
Now we can stop the interview because I only want to talk to people that have [at least] a little bit of understanding about football.
"He puts his hands on him, I don't know why, and we get a penalty and put it in the back of the net".
Turkey condemns 'disproportionate force' by Israel
Many in the global community have been protesting since Friday in reaction to the decision. The Palestinians see occupied East Jerusalem as the capital of their future state.
"I'd be saying: "What [are] you doing?" I couldn't blame our lads too much.
Despite Jurgen Klopp's surprise decision to leave both Philippe Coutinho and Roberto Firmino out of his side's starting lineup, it was the home side who came out of the blocks firmly on the front foot this afternoon, immediately pushing their bitter rivals back from the first whistle. I can keep that for the rest of my life.
The likes of James Milner, Sadio Mane and Mohamed Salah were heavily involved from the off, but struggled to carve out any clear-cut goalscoring opportunities until a moment of brilliance 5 minutes before the interval handed Liverpool the lead that they fully deserved. "I think the performance shows we made the right decision, but the result does not".
The Egyptian winger, who is the Premier League's top scorer, shrugged of Cuco Martina before dancing past two Everton defenders and beating Jordan Pickford with a stunning curler to get Anfield roaring in unison.
Everton next travel to Newcastle United on Wednesday, who are floundering at the moment, while Liverpool host West Bromwich Albion on the same day and will look to put their derby day disappointment behind them against the Baggies, who are near the drop-zone.