Atleti have been contenders for European football's top club prize in seasons past but come into this week's clash with Klopp's Liverpool as underdogs.
Klopp is not so sure, though, suggesting a transitional season at the Wanda Metropolitano following the departures of Antoine Griezmann, Diego Godin and Lucas Hernandez has been solid enough.
"Playing Atletico is one of the most difficult things in the life of a football player," the Liverpool manager told a pre-match news conference on Monday.
"They are really well organized, a result machine, squeezing results out of each game if possible.
"Yes, people tell me this year is not exactly like that, but it's a transition period – that's normal. They're still fighting with all they have. You don't get a lot of chances. It's really difficult.
"What they played so far in the season was not as bad as people say and have nothing to do with what happens tomorrow, obviously.
"The team that will play better tomorrow and the next game, who fights more, who wants more, will go into the next round – not the team who plays the better Premier League or LaLiga season. It's as easy as that.
"But we are here, and nobody doubts that we are pretty ambitious. We will give it a proper try."
Klopp is not interested in suggestions Atleti play an unattractive style, pointing out it is "successful" and therefore appeals to him.
"I have nothing to say to these people, to be honest," he said. "Attractive football is what is successful. For me, it's attractive.
"It's very intense. It's speed, it's aggressive, it's a clear plan, it's a clear philosophy.
"I know we are in Spain, the country of tiki-taka – maybe people say it because of that – but I am from Germany. I admire things like that. For me, I don't have that discussion."
Klopp expects this intensity to cause Liverpool problems if they slip below their high standards.
"If there's a team where you have to be at your absolute best in all departments, it's Atletico," he said. "There are no presents tomorrow, absolutely no presents.
"If you work hard, as hard as possible, then you have a chance. If you don't do that, you don't even have a chance. That's it."
This attitude extends to Simeone on the touchline, with Klopp adding: "People say I'm emotional at the sideline. If I'm on level four, I would say Diego's on level 12.
"It's like I'm the kindergarten cop against him. It's really impressive. It's over all these years. Eight years, really long, having still this emotional level, wow.
"His teams are always world-class organized. That makes him one of the best."