A goalless draw at home to Porto confirmed Liverpool’s place in the last eight – their first for nine years – which was already virtually guaranteed after their 5-0 first-leg victory last month.
Heading into this round of matches Klopp’s side were the competition’s top scorers with 28 goals and he believes that has already proved they can compete on their return after a three-year absence.
“It should not be a big surprise,” he said.
“I never had a time schedule in my mind where I thought ‘we have to be there and then have to be there’.
“Actually, I don’t want to make it smaller than it is, but on the other side I don’t want to make it bigger than it is.
“This year we belong there, to be honest. Next round will be very difficult, that is clear. There will be seven other very good teams, maybe another four from England which does not make it easier.
“I think we will have a chance, for sure, to get through to the semis and that of course is the target.
“Take it step by step. It is cool absolutely. This is our first year when we had the opportunity to do it so I think we are in time.
“We are a little bit satisfied, to be honest. There is a good development in Liverpool, a nice moment.
“It is good, it is done and now let’s carry on.”
Klopp made five changes for the match but played two of his front three in Roberto Firmino and Sadio Mane for 62 and 74 minutes respectively while 32-goal forward Mohamed Salah was sent on for the last 20 minutes.
Critics will question the Red boss’ wisdom in doing so with Manchester United at Old Trafford up next at the weekend, but the German insists he was doing his Egypt international a favour.
“Everyone thinks about injuries but that can happen all the time,” he added.
“Now we thought we give him, if possible, the last 20. If it is 15 he trains again on Wednesday.
“I told him if he really runs a lot he does not have to train so I thought he was quite lively.”
Of the other changes Klopp said: “(Andrew) Robertson had an issue but not big. It was not about rotation, only about the next line-up.
“It was not too intense for Sadio even though he was lively. It was very important for Adam (Lallana), getting used to the rhythm, and for Ingsy (Danny Ings) a few minutes.
“Joe Gomez playing after a few weeks was important. Now we can prepare the Manchester game and I am looking forward to it.”