The Reds took a huge step toward qualification for the Champions League quarter-finals last week as they carved out a 5-0 aggregate lead over Porto in the first leg of the sides' last-16 tie.
Things also look promising on the domestic front, with Klopp's men sitting third in the Premier League - just two points short of second - ahead of Saturday's meeting with West Ham United at Anfield.
But the German isn't satisfied yet, with his sights set firmly on the challenges that lay ahead.
Klopp told reporters: "I am absolutely not happy. I want to be happy at the end of the season. Happy is not the word I have in my mind, to be honest; I am sometimes fine with it, sometimes more, sometimes less.
"Immediately after the game against Porto, it is not good for me as a human being, but I thought about West Ham - that is our life, to deal with that.
"What I want is that we are really ready for this game tomorrow. They will defend a little bit deeper, probably, and we need an atmosphere that is ready for that as well.
"It's nothing decided this season, we are in a good position but a good position only gives you the basis for the next few games and now we have to use it as a group - players, coaches, manager and crowd.
"We need to be ready for a difficult game tomorrow because they - I don't know exactly the results but - drew against Tottenham, lost with one goal at [Manchester] City, stuff like that. It shows you need to do it.
"They always have opportunities with counter-attacks and set-pieces to score by themselves.
"Either way, it’s all negative or when it's positive it's so positive that we don't care about the next thing. I am not like this.
"I really want to use this basis now and, for that, we have to be at our best tomorrow afternoon, so I know it’s a lot of work to do."