Saul Niguez’s fourth-minute strike was enough to give the Spanish side the advantage over the defending champions.
Madrid’s stadium was raucous on Tuesday with fans orchestrated by energetic Atletico manager Diego Simeone.
“Atletico fans who can a get ticket… ‘welcome to Anfield’,” said Klopp.
“Emotions are important. Tonight they were obviously completely on the side of Atletico, but I am really looking forward to the second leg.
“We speak from time to time about the power of Anfield and the power a stadium can have and tonight you saw that.
“It’s half-time and we’re 1-0 down. The second half will be played in our stadium and they will feel it.”
Liverpool did not manage a shot on target against a resilient Atletico side – only the second time the Reds have failed to test an opposing goalkeeper since Klopp took over as manager of the club in 2015.
“I have no problem with the result,” added the German, who has never lost a European two-legged tie with Liverpool. “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.”
- Why ‘exquisite’ Atletico were so hard for Liverpool to break down – Warnock analysis
- Football Daily podcast: How to beat Liverpool? Better call Saul
- How you rated the players
‘We know our fans will be there’
Scottish left-back Andrew Robertson said Atletico celebrated “as if they’d won the tie” and that his team would produce a better display in the second leg.
“We gave them the best possible start and that gets the fans behind them and then they start falling over and getting under the skin a bit,” he said.
“We put in a decent performance and we know we can be better. We’ve got a second leg to put it right. They are coming to Anfield and we know our fans will be there.”
Captain Jordan Henderson, who came close with one of Liverpool’s two openings, was substituted in the 80th minute after picking up an injury.
Klopp added: “Hendo felt his hamstring unfortunately. We have to wait. He was not too concerned, but enough to go off obviously.”
‘The crowd and the side were a block as one’
Simeone was ecstatic with the victory, which came after a poor run of only one win in six matches in all competitions – which included defeat in the Copa del Rey by a third-tier side.
The Argentine said the atmosphere generated by the home support on Tuesday was the best he had witnessed since he came to the club in 2011.
“My side started winning when we came up the road leading to the stadium,” said Simeone.
“We saw players who believed. We saw the beautiful side of football. The crowd and the side were a block as one.
“Winning breeds winning. The best way to feel strong is to win and that’s what we want to do. It was a very important win for the club tonight.
“In the eight years I’ve been here, I’ve not seen the crowd like that for the whole game. It was really emotional.”