Spurs had seemingly rescued a draw from 3-0 down at Anfield, but Diogo Jota came up with a dramatic last-gasp winner to cancel out Richarlison's equaliser in added time.
Klopp reacted to Jota's strike by running towards fourth official John Brooks and celebrating in his face, appearing to pull his hamstring in the process, and he was cautioned by Tierney in the aftermath.
However, the German alleged after the game that Tierney used words that were "not OK" when booking him and believes that the official has something "against" his team.
The FA are currently investigating the incident, but the PGMOL has announced that they "strongly refute" Klopp's suggestions after listening to the audio of his confrontation with Tierney.
Klopp, who is apparently at risk of a lengthy ban for his comments, spoke to the media on Tuesday ahead of Wednesday's clash with Fulham, and he revealed that Tierney told him he would have been sent off had the referee got his way, but Brooks's presence meant that his punishment was downgraded.
"I didn't say anything wrong. I was shouting: 'Without you, without you!' It doesn't even make a lot of sense. That was all. I couldn't get really close to the fourth official... the direction was already not really right and I didn't want to get close at all, because then I felt my muscle, that's it pretty much," Klopp explained.
"Paul Tierney came over to me, I didn't expect at all a red card, to be honest. I know I had a red card not too long ago, I didn't expect for a second a red card because I didn't feel that was right.
"I expected a yellow card in that moment and he said to me: 'For me it's a red card, but because of him...' That's what I understood, it's loud in the stadium, but... '...because of him, it's yellow.' Show me yellow card, smiles in my face. That's it. 'Red card, for what?' That's how I left.
"I said what he said to me was not OK. And actually I thought it was not OK because it was not a red card in my view. That's it. And then the things happen, I understand, I opened the box with that.
"I know he's not doing it intentionally, but we have a history and I cannot deny that. I'm not a resentful person, not at all; not at all. I think it's a waste of time.
"I had to get over so many things in my life and I get over them. But obviously these kinds of things what happen in the past in decisive games for us, if you were involved or not, they happened.
"The whole situation is off, it shouldn't have happened at all, that's how it is. It was out of emotion. It was out of anger in that moment, never a good leader for the things you do."
Jota had been classed as a doubt for the game before coming off the bench to score the winner, but Klopp has now revealed that the Portuguese has sustained another knock and is touch-and-go for the visit of the Cottagers, while Naby Keita and Roberto Firmino will also miss out again.
"In our situation Bobby is out and Diogo struggles. He got, in the West Ham game, a knock in the back, a bruised rib, could not train before the [Tottenham] game but could play without an injection or whatever, but got another knock immediately when he came on," Klopp added.
"You might have seen the celebrations of Diogo, he was sitting down pretty slowly. He didn't train since then so that is one that is a doubt... he is a doubt at least but I hope he can recover until tomorrow night."
Stefan Bajcetic (adductor) and Calvin Ramsay (knee) are also out of contention for Liverpool, who sit fifth in the Premier League table as they search for a fifth top-flight victory on the bounce.