An early goal from Saul Niguez saw Liverpool fall to a first defeat in any competition since December, giving Atletico the upper hand when the teams meet again next month.
Speaking after the game, Klopp advised Atleti of the challenge they will face when they travel to Merseyside for the second leg.
“It's half-time and we're 1-0 down. The second half will be played in our stadium and they will feel it,” Klopp is quoted as saying via BBC Sport.
“Atletico fans who can a get ticket...’welcome to Anfield’. We speak from time to time about the power of Anfield and the power a stadium can have and tonight [Tuesday] you saw that,” the Liverpool boss added, reflecting on the atmosphere at Wanda Metropolitano.
“I have no problem with the result. I saw so many happy faces at Atletico, but it’s not over yet.
“I’m not sure what we have to be in the second leg. They were going constantly to the petrol station and we drove with one tank. I’m not sure if Diego Simeone saw a lot of the game because he was continually animating the crowd.”
The defeat leaves Liverpool with plenty of work to do if they are to qualify for the quarter finals, though their European record under Klopp shows they're certainly capable of overcoming the first-leg deficit.
Though they saw off Porto and Bayern Munich with relative ease in the knockout stages last season, they needed a remarkable 4-0 win over Barcelona at Anfield after a 3-0 Camp Nou loss to reach the final, where they would beat Tottenham 2-0 at Wanda Metropolitano.