Jermain Defoe twice equalised from the penalty spot, cancelling out Daniel Sturridge in the first-half before later pulling the Black Cats even again, following Sadio Mane's close-range poke which had put the Reds ahead a second time at the Stadium of Light.
But Klopp, who admitted his side's concentration was below-par with this their second Premier League game in less than 48 hours, insisted he didn't agree with referee Taylor's decision to award a free-kick for a supposed foul on Defoe in the build-up to the second penalty.
There was no contact on Defoe, bemoans Klopp
He told journalists afterwards: "If you see it again, there was no contact. I saw it in the game, but that was the decision. It was not the worst mistake in the world, I don’t want to say it is."
Yet the German added that the "harsh" decision is why the result "feels so hard" and insisted that he "usually" can be "really clear" in his post-match team talk if his players "are responsible" for the result.
However, Klopp said on this occasion he said he had "no idea" as he explained that "on the one side" he came away "proud of them for what they did, how they worked and how they fought" and yet disappointed "on the other side" because his team, he says, "can play better football."
Klopp insisted that he had "no idea" whether "it would have been possible" to play better against Sunderland, calling it "really difficult" and saying: "In a situation like this - and Sunderland were in the same situation - you always need a little bit of luck."
The manager believes that Nathaniel Clyne "could have been [given] a penalty" after an apparent shirt pull from Sebastian Larsson but acknowledged "that's how it always is" and "how it feels with penalties" as "sometimes the referee sees it and sometimes not."
He conceded that referees face "a really difficult job" and that "both [penalty] decisions are right", but vowed: "That's how it is. [To concede from penalties] Twice is so hard. But I will accept it, no problem."
'Conceding two penalties doesn't feel good'
The Reds boss said that, having beaten Manchester City in a huge clash at Anfield just two days earlier, settling for just a point in the north east was difficult as their momentum again went to waste - although they have only lost once in their last 18 league outings.
He declared that "in this moment" it was "really hard" to accept the result, but admitted that he has to come to terms with it because he is "professional."
Klopp declared that, despite the result, the title race "obviously" is "not finally done" and admitted that his demeanour post-match might make him come across as "not the best loser in the world", which he has "no problem with" because "two penalties feels not good."
"I usually like to talk about football, but it's difficult today," continued Klopp. "I know what I can expect when I say [to the players] 'that was not enough' or 'that was enough' but today, if I said 'that was not enough', I have no idea if they could have done more. That's my lack of experience."
Reds boss: It's hard to accept it, but we will
Klopp pinpointed Liverpool's dominance of the game, having spurned a handful of chances, as one such source of frustration for not coming away with three points.
He noted it as "completely difficult" to assume anything about the game going into it, because he hadn't had any "experience in situations like this" with the fixture coming so soon after the team's last, meaning he had "no idea what I could have expected from the performance side."
The manager felt his charges "started really well" but then "lost concentration" which he said is "not usual" for the players although it has "happened before", Klopp suggesting that it was maybe "because of the fixtures" although stating he was "not sure."
Klopp said that Sunderland "came a little bit into the game" and mentioned that beforehand it was "clear" that it would be "difficult" to play Sunderland away from home, citing their "good transition game" with Defoe and former Reds striker Fabio Borini, and stating how their first goal came "after a throw-in" showed that.
He said that Liverpool "again dominated the game" in the second-half, explaining: "Usually I would say we could have done better, but I don't know exactly if we could have done better because I was not in the boots."
Klopp insisted that Liverpool's second goal "felt good" and "felt deserved" but, on Sunderland's second of the afternoon, said: "I would say no foul, but a free-kick [was given]. I saw it again - no contact [from Lucas Leiva or Emre Can on Defoe]. Then handball, 2-2."
Yet Klopp said that's "how it is" in the Premier League and it "doesn't feel good", stating that his disappointment was not "because of the point" but because "of two penalties in the game."
He felt in particular the free-kick was "harsh and really hard to accept", despite acknowledging that he "obviously" has "to accept it" and "will."