Mo Salah's deflected effort had put the Reds in front but Spurs battled back courtesy of Heung-Min Son.
Speaking to Amazon afterwards, Klopp enthused over the efforts of his players, saying: "It was absolutely deserved. It was a really good game against a top side.
"They’re a top counterattacking side. If you lose one ball, you end up 80% of the time in your own box. They don’t want the ball too much so you have to play around them. You have to keep them busy and the boys did that very well."
"They scored a goal, which is a typical Tottenham goal, and had two or three more chances, but it felt like we had 70% possession, and that makes it tricky to stay concentrated.
"We scored a nice goal at the end, a sensational header from Bobby at the end.
We have to push ourselves."
Klopp also took time to praise Mourinho's side and refer to them as one of the challengers for the title in this closely-fought Premier League season.
He added: "Spurs are 100% one of the favourites. In these top games, they’re not bothered to sit back and counter. That’s really difficult to play against. They will be there until the end of the season."
Klopp referenced the performance of youth graduate Reece Williams, who produced a memorable performance against Harry Kane throughout.
Klopp: "Oh my God! Outstanding, outstanding! Reece Williams! He played against the modern day Alan Shearer, Harry Kane. He dropped in the right moments.
"Second half, they avoided Reece and played long balls towards Fabinho, they put Harry there.
"He’s got the right amount of confidence. He kept it simple, made super challenges. An absolutely incredible game. He’s already here for years and wants to stay."