The Reds reached the final eight after drawing 0-0 with Porto last night, progressing 5-0 on aggregate.
Klopp felt it was time his side Liverpool showed up in the latter stages of the competition again and said it was important so that others could see the development his team had made.
"It feels good to be honest, feels really good," said the Liverpool boss.
"I cannot feel what people feel who wait so long for it. But it feels good so I know about it.
"Last eight is cool. We're not a little bit satisfied to be honest. But I think it was time that we showed up again.
"Good development in Liverpool in the moment, nice moment but if you don't show up in a competition like the Champions League no-one really will realise it.
"I'm happy for all the people involved that we made that step. It's done, it's good and now let's go and carry on."
Klopp addded: "I didn't have a time schedule in my mind and think 'we have to be there, or we have to be there'.
"I don't want to make it smaller than it is but on the other hand I don't want to make it bigger than it is.
"I think this year we belong there to be honest. It should not be a big surprise."