The Premier League team had been in dire form domestically under sacked manager Thomas Frank, while at the same time impressing in the European competition. They ended in fourth place on the group stage table, behind only Arsenal, Bayern Munich and Liverpool.
But under new interim boss Igor Tudor, the club have lost their last four games, including their one-sides clash with the Spanish giants, that saw Spurs three goals down after 15 minutes.
Tudor opted to hand inexperienced goalkeeper Antonin Kinsky his Champions League debut but hauled him off with 17 minutes played for regular keeper Guglielmo Vicario.
Marcos Llorente had opened the scoring after just six minutes, while Antoine Griezmann slotted home from the edge of the area after some sloppy defending on 14 minutes.
Julian Alvarez slotted home a fourth past Kinsky, while Vicario couldn't keep out Robin Le Normand shortly after his introduction.
Spurs pulled a goal back through Pedro Porro after 26 minutes but Alverez bagged his second of the night to restore a four-goal cushion.
Second half substitute Dominic Solanke gave Tudor's side a glimmer of hope of overturning the score in the second leg with his goal on 76, but it remains to be seen if the manager will still be in place by then.
The second leg takes place at the Tottenham Hotspur Stadium on Wednesday 18 March.
Reflecting on the game, Atleti boss Simeone said on IntotheCalderon: "I liked the team, we had an impact that was helped by the mistakes we forced them to make, which gave us confidence, encouraged us to keep pressing in the opposition's half and take a significant lead.
"From (the possibility of the scoreline reading) 4-2, which happened with Oblak's save (on Richarlison), there was an extraordinary transition between Griezmann and Julian, with good teamwork, a 50 or 60-metre run and a finish, which put us in a good position in the match.
"But then the 5-2 came from a mistake on our part, and we enjoyed the victory knowing that the Champions League is complicated and no result guarantees you will go through in the first match."
"I always focus on the good things. Offensively, (Spurs) have important qualities, they have tall players on set pieces, even their throw-ins are dangerous, added Simeone. "We went into the match in a way that took them out of their comfort zone, and that speaks well of our work."
Spurs boss Tudor said on TNT Sports: "Strange game. We give them three goals. We restarted good but then the problems kill us. Very, very strange, very unusual. It took our confidence.
"We apologise to the fans who were here today, to everyone. They had a difficult moment."
Tudor added: "Everything looked like it was going wrong, every small mistake we pay, even the situation at the end, two players out. Everything is going against us.
"I need to help. I need to keep working, not speaking too much, to stay focused on things we can do.
"It's difficult to explain, it is the first time I see this in my career of 15 years, so what can I tell you?
"My focus is on the problem, the players also, so we need to stay positive."