Despite Diego Costa pulling a goal back, Klopp's men held on for a deserved three points which moved them up to fourth in the Premier League.
The former Borussia Dortmund boss told Sky Sports: "It was satisfying, especially the first half, it was brilliant.
"We started the game from the first second. We had unbelievably good movement in our playing side. Everyone who plays against Chelsea knows it's difficult to play against them, they are really well organised, but we created the space and played in them.
"It was a deserved lead at half-time. Before half-time there were times when Chelsea were a bit better in the game but only because we stopped playing football.
"The beginning was brilliant from my side and we played football that was really nice to watch."
Klopp also believed that man-of-the-match Jordan Henderson deserved his match-winning goal, adding: "It was really nice and it was deserved. He's a hard-worker and he's still a young lad and a lot of pressure on his shoulders and we are helping him to learn how to handle it and he's getting better and better and better."