The Reds will take on Arsenal at Anfield in the next stage of the competition after goals from James Milner and Ki-Jana Hoever at Stadium MK.
The tie saw Klopp hand competitive senior debuts to Caoimhin Kelleher, Harvey Elliott and Rhian Brewster, with Herbie Kane and Sepp van den Berg also coming on as substitutes to make their bows for the club.
Read on for a summary of the manager's post-match press conference...
On the performance...
Very good moments, couple of individual performances. [For] 75 minutes we controlled the game, so then it was really tricky. Kelleher, to be honest, these games are there so the boys show how good they are. For a goalie, it's quite difficult in a game like this but then being there having not a lot to do over the whole game and then having these kind of saves, that's absolutely brilliant, so I'm happy about that as well. We could have done better, of course, in that period, there's no doubt about that. But before that we controlled the game, we started well as a team but then we got a bit stiff because we didn't score. An early goal would have helped, we have to force the goal then obviously.
The team tonight was a team with a lack of rhythm and a lack of experience. The most experienced and the player with the most rhythm was the best player on the pitch - Millie was pretty obvious. But it's so important that we still do these games, that we are brave enough to use the boys. We are not here with this line-up because we don't respect the competition, we are here to win the game, no other reason. We don't fly to London with all that stuff and then say goodbye. So I am really happy that we went through, that's cool and that the boys felt adult's football as well, that's really important. Very physical situations for offensive players especially, not overly hard, but hard challenges. But still they could show in moments how good they are, so big step for them and I am really happy. All good.
On Milner setting such a good example...
Absolutely. This man is on fire, that's how it is. It helps a lot. He's a real role model for young players. If he could play every day, Millie would be like this every day, that's how it is. Absolutely brilliant.
On Harvey Elliott...
16 years old still and this kind of football is good, really good for us. Brilliant boy, takes the situation really well, wants to learn. Tonight, he will always be a special player for moments, but his overall performance when you see him defending, when you see his movements are so smart, it's not easy to outplay him. That's really, really good and his left foot is not too bad. A bit unlucky, otherwise he would have scored. Good player. They are all good, we don't have bad young players, to be honest. They are all really skilled, so that's why it's so important we can give them these matches. We will try to continue like this. We will see.
On Hoever's goal...
It was [a brilliant finish]. I didn't play when I was 18 years old on a similar stage, so it was quite impressive. The atmosphere was good, it's a big stadium - a really nice stadium, by the way, I wish other clubs in London would have had similar dressing rooms! The first half was very, very defensive-orientated stuff and I'm not sure if he was very often in the box. But when he was needed in the other box, he was there and a wonderful goal, wonderful cross. Absolutely good.
On whether Hoever's long-term position is full-back or centre-back…
There is no reason to decide that now because for the moment he can play both for sure. Full-back is a little bit better for him in the moment, we have to see how he develops physically because the centre is a very demanding position. You have to be physically 100 per cent ready. He has the speed, he has the passing, quality. Crossing can be improved, but he has a lot of skills that are necessary or useful in the full-back position. He has speed, but in the things he has to be more natural, desire to go in the right direction, open up when you control the pass already so that you see the pitch. There are so many things to improve, but it is normal. He is 17 years old and if he couldn't improve anymore that would be really strange. He has the most time and hopefully we use that together with him.
On the development of Liverpool's young players…
We don't have to make them now quicker and bigger than necessary. They all are good but there is no reason to say now if someone is not in the same level in this moment then he is not there in a year or so. There is no reason. They all have the right environment so we will improve that environment as well, we will bring in more manpower there that we can really take care of these boys more. That's really important. We believe in them but they have to make the next steps. I told them after the game, the last 10 minutes, these boys are naturally fit but you saw it was not the game anymore. They lost it and that's not OK. Then you see Millie is running around, you have to feel it on the pitch - that's why it's so important. Whatever I tell them is not the same if they see it on the pitch.
On his impression of MK Dons and their performance…
Good in the end. They changed a lot, they grew in the game. Before the game, I think they'd played 5-4-1 in the last few games in the league. They changed the system for us tonight and changed it in the game again. They had a lot of chances in the end, so that's all good. They are physically very strong with smart strikers, I would say; they use their bodies really well. With a bit more speed from us in passing and stuff like that I think they would have had more problems because we had good situations in the one-on-ones; Millie first half, Curtis in the box. If we are a bit more clear in these situations then we can score earlier, but that's how it is. They did what they could and the whole project looks really nice, I hope the rest of the club is as good as the team and the stadium. Then there is really a positive future there. It was good fun tonight coming here, the supporters were on the side of their team but not overly against us I would say, they enjoyed the night. Because we controlled the game so much, it only really became exciting for them in the last 10 minutes. We go into the next round and it was nice at MK Dons.
On Naby Keita's performance after his return from injury…
Obviously he looked good in moments, he looked really good in moments, but he has to adapt to the position again. You see it with Ox as well. Naturally you move much more and stuff like this, you find each other much more, but that's how it is. He was out for a while, but in moments you saw what an incredible player he is and how important he will be for us. We don't have to rush it now hopefully, but we can use him now and that's good, good for us. There's a long season to go and everything will be fine.