The Reds played out a four-goal encounter with the visitors, and were forced to come from behind before Wanderers secured a third-round replay.
Goncalo Guedes put Wolves in front at Anfield in the 26th-minute though Darwin Nunez and Mohamed Salah both struck either side of the half-time interval.
Substitute Hee-Chan Hwang, though, saw his effort shortly after the hour restore parity and earn a draw in L4.
Read on for a summary of what Klopp had to say in his post-match press conference.
On the result and performance of his side...
[It was a] good start in the game, dominant, played well, tried to create, had half-chances, good moments. Twenty, 25 minutes around about - I don't know exactly when they scored - before they scored they had maybe one counter-attack and then they had this scrappy situation where it was not 100 per cent clear around the goal. We win the ball there and then Ali kicks the ball in their feet and then we are 1-0 down.
You could see the impact on the game; they got more confident. We played kind of OK, not really convincing that you thought, 'OK, it will happen immediately.' The goal we scored was outstanding, outstanding, and we had a few really good balls we played, a few good situations where we played in their formation. But for the whole game I thought we didn't win enough challenges, to be honest. There are a lot of situations where I thought they win a challenge and all of sudden we are completely open; we had two or three players in the challenge moving to the ball and when you are there, fine, you have to win the ball. If you don't do that and they can get out then it looks like, 'Where are they?'
So, they constantly stayed in the game because of that, but we anyway went 2-1 up. It was not an open game, but nothing really happened a lot, but we still kept not winning these challenges, like around the second goal when I think we were in possession and had the ball, gave the ball away and then they go in our box without a real challenge. That's difficult. The ball comes in and it's difficult. It was unlucky, Ibou is there but it hits Hwang and then the ball rolls over the line. Unlucky, 2-2 and that was the result.
On Wolves’ disallowed goal in the second half and his understanding of it…
I don’t really know. On the pitch I couldn’t see it, so I had no idea. For me, I thought it's a goal. It was the player in the left corner who might have been offside. We have one angle, which I saw in the dressing room, where it could be offside but I would not swear on it, or however you say that, but it could be. But I think this angle the VAR didn't have, if I'm right, that’s what I heard.
There is a similar situation in the Arsenal game where one angle was missing and in the end everybody thought it was [a] clear offside, but we couldn't prove it because the angle isn't there. I don’t know how these things can happen, but it happened. So, I understand the frustration of Wolves because you want to have the right decision in these moments, like we wanted the right decision back then. But I cannot say anything about it because I have only saw one camera perspective and that's it.
On the replay with Wolves and whether he is 'thankful' for it...
I know where I am coming from, but the situation is that we could still play extra-time, or [a] penalty shootout, and the game is decided tonight. So, we deserved not more than a draw tonight and whatever the consequences are, in this case it's now an extra game, so that's fine. I have no problem with that... somebody told me that they will be decided about, or whatever, that somebody will talk about it if they scrap it... there was a discussion, I didn't start the discussion, I got a question and the question I don’t think we should have them, but I knew we still have them. It was clear that we have now to go to Wolves; Wolves [are] probably in this moment more happy about it than we are, but until then we will be happy enough to give it a go.
On whether he is ‘concerned’ by his team's defending in general…
Not in general, but in moments, it's not concerning... look, you watch a game and then you see the things that happen. Whatever you play, high-line, deeper-line, ball-orientated, man-orientated - you have to win challenges. There is no alternative to [that]. So, yeah. I mentioned already now in the dressing room and I will mention it again and the next team we face is Brighton, who are meanwhile famous for playing proper football. If you don't defend properly there, then why should we go there?
I can understand, it looks open in moments, but it is just open because we think we win the challenge and then we don’t win it and that's then really tricky to deal with in the end. It's not that they had now chance after chance, what it causes us is a lot of effort to put it right in the end and if you are already there, so you could win it where you are, then you don't have to run back and try to solve the problems there.