Saul Niguez's fourth minute goal saw the Reds lose 1-0 at the Wanda Metropolitano Stadium, meaning they have work to do in the second-leg of the Champions League last 16 tie at Anfield.
On what was a disappointing night for the reigning European champions, they also lost Jordan Henderson and Sadio Mane during the course of the 90 minutes, raising concerns over fresh injuries for the pair.
When asked about their condition by BT Sport after the game, Klopp confirmed that Henderson was withdrawn due to a muscle complaint.
"He felt a hamstring. I hope it was a precaution, but we will have to see", said the German manager.
There is some relief regarding Mane, however, with Klopp revealing that he was substituted at half time as he did not want to risk him receiving a red card having already being cautioned in the first 45 minutes, while he also says he felt that Atletico gave the Senegalese forward some rough treatment in an attempt to rile him up.
"He was targeted, obviously", Klopp said. "Sadio played a really good first half and the only thing they wanted is to make sure he gets a yellow card."
Mane was booked in the 40th minute after a clash with Šime Vrsaljko, one of three Liverpool men, including Klopp, to be cautioned on the night.
The Spaniards, meanwhile, received just one yellow card, a statistic that didn't sit too well with the the boss of the Anfield club.
"You need to be really strong as a ref in this atmosphere", Klopp added. "Obviously it was not easy, so many things happened today. I think after 30 minutes three players of their were already on the ground just to have a little breath or something, I don't know, nothing happened.
"The first yellow card was for a striker from us, in this game. I'm not sure they even got a yellow card and that's really funny."
The return leg of will be played on Wednesday 11th March, when the Reds will be hoping to overturn their one goal deficit and keep up their record of never losing a two-legged European tie under Klopp.