But since he replaced the injured Spaniard in December, Robertson has established himself as Klopp's primary left-back.
And the Scotland international continues to validate Klopp's decision by playing like how he did in Portugal.
Klopp said: "It was really good. The whole package, offensively and defensively, was really good. I would say it was his best game.
"We didn't speak before the game about his debut, we handled it like business as usual, and he did really well.
"I saw him in the dressing room before the game deep breathing - it's special, it's really special.
"At the end it's only a football game but we are all human beings and we are [affected] by different circumstances and when you hear the Champions League song before the game.
"I remember my first time, it was really different to all that you've had before because for a football player it's a dream.
"When he played in Scotland or in Hull it was quite a distance to go to a Champions League tie and now he played it - and in that manner, even better."