The Reds are unbeaten at the halfway stage of the Premier League term, having amassed 51 points from their 19 games so far to position themselves six clear at the division’s summit.
In addition, just seven goals have been conceded, but Klopp remains adamant there is further development and enhancement to come.
Asked if he felt Liverpool had reached their potential, the manager told reporters: “No. We had our moments. We had very good moments. There are a lot of really good parts but was there a game where I thought, ‘It is not possible that we can be better?’ No. It was not there yet. We have to improve in pretty much everything.
“There is a lot to come from the boys, but so far the steps are really OK.
“It was said we lost a bit of our spectacular [style] when people were asking, ‘It’s good you don’t concede, but where is the free-flowing football?’ and I sit here and think it is like a kid getting a nice present for Christmas and then asking, ‘Where is the other one?’
“You always want something else or a bit more. We had to develop. It’s not a new style, but we had to step a bit aside to start again.”
Liverpool’s 4-0 win over Newcastle United at Anfield on Boxing Day meant they reached the midway point of the season still unbeaten, with other results in the Premier League helping them move six points clear at the top – and seven ahead of reigning champions Manchester City.
However, Klopp isn’t interested in any talk of the Reds being favourites to hoist the league title aloft.
“Nobody celebrates the half-time whistle of the season,” he stated. “It gets really exciting when you have five games to go and you are six or seven points up. People don’t see it, but I’m a pretty calm person. Not during the 90 minutes but in general. I don’t get that easily excited about different things. It’s only about us.
“If we lose a game people will immediately see it as slipping through our fingers again or whatever, and that’s just not our situation.
“We have to train, we have to work, we have to play, we have to fight, all these things and try to make the best of this season.
“We were not the hunters and now we are not the hunted or whatever. We are just a football team who want to play the best season of our lives. But that was actually the plan last season as well and the year before. You can always make the next step, especially with the quality we have around.
“You need luck with injuries and you need luck in games. You can’t always have influence on it. You see the players are now more mature, 100 per cent, but that’s normal. We brought fantastic players in and all the other players matured here.
“We had difficult situations. Losing those finals is not nice. It’s not like we go out the next day and say, ‘What happened yesterday?’ You carry it with you.
“Even defeat in a final is good for something and you learn from it. It has been a year with a lot of highs and a few hard, hard lows, but a better year for Liverpool, for sure.
“Going to the Champions League final was a brilliant ride. Of course, we had the massive low in Kiev, which was hard to take. You smell how it feels when you are that close, and you want to go again.”
Klopp added: “It’s just the position we have is absolutely good. But we play Arsenal and in five days, we play Man City, so why are we talking about points we have and points we don’t have? I don’t feel like a [league] leader, we don’t feel as leaders of it. There is absolutely no difference.
“We have to play the best football we can play. If we play an 80 per cent game against Arsenal, we lose 100 per cent. That’s our situation. All the rest is talk.
“The first part of this season was better than we expected points-wise, that’s clear, you cannot plan to get 51 points in late December, it’s not possible.”