The Reds have won all of their seven home games so far this season and are top of their Europa League group having won all three matches so far.
The German is aware that the signs are encouraging however he reminded supporters and journalists that there is still a long way to go until his team are where he wants them to be.
“I think it is really easy to fall in love with this team because there is so much excitement in it.
We have to make massive steps, we have to grow, we have to get more stable.
We have to do a lot of things but a lot of signs are really promising. That's true as well. How the team interacts with each other is really nice because when you talk about the rebuild of a team then it is all about the things you see on the pitch.
Obviously, but to see that there must be a rebuild off the pitch as well – and that's going really well. Players growing into their new roles, if you want. That's all good.
But besides that, nothing really happened. Imagine if we didn't win all three games in the Europa League and everybody would tell me, 'How can you not?' so it's always small margins.
So far, it's OK and before we play Toulouse again we have three games. There is a lot that can happen between now and then, and I would like to play them all one after the other and not making too big steps.”
The performance against Toulouse
The 56-year-old was satisfied with his team's performance against Toulouse and had no grievances with the way his side played.
"Result good, performance good. Especially a lot of really good individual performances which is nice, because it is important for development.
Besides the goal we conceded and the chance we gave them and Trent had his spectacular save, around that, everything what we expected.
Toulouse is a good team and we put a proper shift in, that is what I wanted, the goals we scored were wonderful, I would say the right players scored the goals.
Nothing to complain about, really.”
On the Dutchman's performance, the German was keen to stress that there is still room for improvement but he is happy with what he has seen so far.
“I really like him as a boy and as a player, and it's really nice to see how much he starts believing in himself again.
That's obviously very important for each player but for a young player especially. So that's cool.
Lots to improve still. It's good news because everybody sees the good signs and the potential he has but there's so much more to come, so that's good."
Japanese midfielder Endo notched his first Reds goal but that was not the highlight for his manager.
"I like a lot of individual performances but I would like to mention Waturu Endo.
I'm not sure people think that's spectacular or whatever, but the forward passes he played tonight were absolutely incredible and how often he broke lines with one touch was absolutely insane and then he scores a wonderful goal.
Which helps each player – even a more experienced player. So that's really cool. He would have got a similar hug if I would have taken him off.”
Finally, Nunez, who seems to have adapted to the demands of being Liverpool's number nine after a tough first season, brought his manager a lot of happiness with a spirited performance.
“He played incredible. Honestly, in this moment, I couldn't care less that he hits the post in that moment because everything before was super-convincing, was absolutely clear.
How he took the defender away, how he passed the goalie, it was a perfect situation. He played really good.
The goal he scored, the situations he was involved in, dropping into midfield, staying on the ball, all these kind of things.
There were a lot of good things and he's in a good moment and that's for us obviously important. Really pleased for him with the performance.
Yes, it's a bit of slapstick that the ball doesn't go in and then Ryan finished it off, that is cool. I said it before the game, he's a happy boy or man in the moment and you can see that every day. And now we have to make sure that it stays like that.”
The highlight of the night for the German, however, was the performance of several academy players who were given a chance to shine under the lights at Anfield.
Luke Chambers made his first start, Calum Scalon and James McConnell made their first-team debuts off of the bench and Klopp admitted that he would have liked to have played more youngsters if they were not injured.
“They all deserve it massively.
Luke had a long injury. He had a really good year last year in Scotland, was a lot of interest there in the summer but I didn't blink for a second and then I thought, 'Oh come on, let him go.' Because I really think that in the moment our Under-23s when they are all together, that's a super-strong side and that's important as well.
They train with us. The session we had yesterday, the minus-one session, a proper minus-one session – in the longer period between Premier League and the Europa League then you have a proper session – you don't get that somewhere, this quality, and stuff like this.
So it's really important that the boys go through that as well. Pleased for him. I wouldn't say Luke is in the moment in a top, top, top shape because of the injury and because of another little setback. But we 100 per cent believe in him and trust him, and I wanted to show that tonight.
On the position the next one is knocking on the door with Calum. Everybody could see a really exciting player, had a few situations where he was maybe too excited, but a real talent, a real talent and a real heart for football.
James played a sensational pre-season for us. We gave him a new position, put him on the six, and he did really well there because he's very smart and he deserves it as well.
If Ben Doak would have been available tonight, he would have got minutes, like Bobby Clark probably would have minutes, so that's how it is.
We should not forget Jarell Quansah, who played again.
So a lot of good boys coming up and it's not enough that I tell them what they do from time to time – not too often but from time to time – but sometimes you have to show it. Tonight we had the opportunity to do so and we did, and that's good.”