Robertson made the £10 million switch from Hull City in the summer, with the Scotland international expected to take over as Klopp’s first choice.
But with Alberto Moreno in excellent form this season so far, Robertson’s minutes have been extremely limited, and he has only been in the matchday squad on seven occasions.
Moreno looks to have a firm grip on the starting spot under Klopp, which has already cast doubt over his competitor’s future at Anfield.
Speaking while on duty with Scotland, Robertson admitted to his frustrations at playing such a peripheral role, and revealed discussions with Klopp over developing his game.
“I’ve spoken to the manager because I felt as if the settling-in period was over for me and I thought I was ready to play,” he told reporters.
“I felt I did myself justice in the games I have played so I had a good chat with him.
“He gave me a few points to work on and that’s kept me going.
“I know I’m still well in his plans and if I work on the things he’s asked me to then hopefully I’ll be in the first team, or closer to it.”
Robertson played the full 90 minutes in Scotland’s 1-0 friendly defeat to the Netherlands on Thursday night, lining up opposite Georginio Wijnaldum.
However, this taste of action has clearly not satisfied Robertson, who will be looking to gain a foothold on the club stage in the coming months.
“I hate not playing. It’s been a very frustrating three months for me,” he added.
“I was looking forward to the Holland game to get some game time. I was delighted to get 90 minutes.
“I was a bit rusty and it probably caught up with me in the last 20 minutes but that’s something I’ve got to look at.
“I need to get more game time. I’ve not been used to [not playing]. In the past five years my rise has been good.
“If I can keep doing what I’m doing then hopefully my chance will come.”
It is difficult to see Robertson usurping Moreno as Klopp’s first-choice left-back, and the Reds’ early exit in the League Cup will have done harm to his chances.
But he certainly impressed in his three appearances for Liverpool to date, and the hope is that Klopp manages to rotate both him and Moreno to ensure both are content with their roles.