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.