The Argentine is still reeling after learning that the former Barcelona boss had lost his lengthy battle against cancer
The former Barcelona boss passed away on Friday after a length battle with cancer, sending the entire footballing world into mourning.
Simeone, for his part, cannot believe that one so young has been taken so soon.
"I feel pain," the Argentine admitted. "A colleague has left us. I knew him and I feel the pain of all of us who knew him.
"It is the time to be close to family, remembering him in the best way possible and the best things that he has left us.
"It is a tough loss, he was only 45 and I'm 42 ..."
Simeone was speaking ahead of Atletico's crucial Liga match with Valencia. The trip to Mestalla has come right in the middle of their Champions League semi-final tie with Chelsea, which is delicately poised after last week's 0-0 draw at the Vicente Calderon, but the former midfield ace says his players are concentrated solely on the task at hand.
"When Tuesday comes we'll talk about Chelsea," Simeone stated. "The league is different and we have to be strong. It's in our own hands and we are going to maintain the same rhythm of play and intensity.
"We have to be careful, we have difficult opponents [Real Madrid and Barcelona] fighting and it's plausible they could win every game that they have left.
"We mustn't pressurise ourselves, though. We go from game to game, we can't look any further than that. We have to think about our game, beat our opponents who will also want to win the game."
Indeed, Simeone insisted that while he might make changes for the Valencia game, Atletico will strive to produce their very best form.
"It's another final," the declared. "We have always tried, even when we've made changes, maintaining competition and for this game nothing is different.
"The only thing that's important now is Valencia, Valencia, Valencia. Then we will have three days before the next game."
Simeone also shrugged off allegations that Atletico are nothing more than a counterattacking team with a style of play that is not aesthetically pleasing.
"We try to play with the characteristics of the players we have," he countered. "We're not perfect and we try to prevent errors and use our strengths. Like it or not, we have a style of play."
Atletico currently sit four points clear of Barcelona at the top of La Liga and are chasing their first Liga title since 1996.