"The coaching part is beautiful and tough at the same time," he says. "It's difficult to disconnect. I go to the movies on Tuesday or Thursday if I have a match in Europe - and suddenly the film gets boring and players appear on the screen. I start to think, how can I drop this one, how can I make him improve."
Midfielder Simeone became a cult hero for his performances on the pitch when the rojiblancos last won the league (and the cup) in 1996, bringing 250,000 out onto Madrid's streets to celebrate.
Simeone returned to Atleti as coach in December 2011 when they were 10th in the table, four points above the relegation zone and ejected from the cup by lowly Albacete. They'd just sacked Gregorio Manzano, who'd been there just six months, the 49th managerial change under the current ownership regime.
He's utterly revitalised the club since, with year on year improvements. Tonight, he'll lead Atletico to their first European Cup semi-final since 1974 with the first leg against Chelsea in the Vicente Calderon, the club his side defeated 4-1 in the 2012 European Super Cup.
He'll do so as the man in charge of the Spanish league leaders - an implausible situation at the start of the season when everyone thought that Spain's Primera Liga was a two-horse race. With four games to play, Atletico are four points clear at the top of the table. Atletico are not paupers, but it's a staggering achievement on a wage bill a quarter the size of Madrid and Barcelona.
Simeone has become one of the most highly rated managers in world football, one linked with the vacant Manchester United job following the dismissal of David Moyes. He can't speak English and has only said publicly that he'd like to coach Inter and Lazio, two of his former teams in Italy.
He's renewed his Atleti contract until 2017, but says: "Contracts exist to be broken. I give great value to the trust which Atletico have given me. I have a contract for four years, but I always think they are going to fire me tomorrow, so I only focus on winning on Sunday. I live that way."
He'd also like to coach Argentina, where he won 106 caps, "when I'm 60".
It wasn't easy to leave his family behind in Argentina. When Atletico came looking for him to take over, Simeone phoned his nine year old son Giuliano at the family home in Buenos Aires.
"Dude, I have to tell you that Atletico Madrid called me. They want me as coach."
"Really? You'll get to go against Messi and Cristiano Ronaldo?" replied Giuliano.
"Yes, sure, but I have to move to Spain."
"But we'll be able to see the matches?
A long silence followed. Simeone knew that his family would have to stay in Buenos Aires. It was too risky to keep moving them around the world with different jobs. Besides, all three of his sons are footballers with River Plate: the eldest, Giovanni, 18, is just breaking into the first team, Gianluca is a younger player at River. He knew that nothing would be more painful than losing day-to-day contact with his boys and his ex-wife, a model. Guiliano realised that he wasn't moving to Spain.
"If you win, you'll not come back," he said.
"That killed me," said Simeone, "I didn't know what to say."
Atletico's manager has never stopped winning. His players and fans adore him with a reverence not experienced by other managers.
Simeone's predecessor, Manzano, had lasted six months, but his attempts to rebuild a side after the sales of Sergio Aguero, Diego Forlan and David de Gea in 2011 had faltered, though a bright spot had been the form of ÿ40 million new signing Radamel Falcao.
Asked to compare Manzano with Simeone, the Brazilian Miranda, the defender who scored Saturday's key opening goal in the 72nd minute of a nervy league match against Elche, said: "There's no comparison. It's like I moved to a new team.
"Simeone is a great coach and is always trying to take the best of every player, our side is 70% better now. All we've achieved these last two years, we owe a big part to him."
Despite saying that things "need to be taken slowly", 'El Cholo' - a nickname bestowed by a former youth coach who reckoned he reminded him of former Boca player Carmelo Simeone - quickly began a transformation. Others would call it a revolution.
Simeone said he wanted to 'see an aggressive, strong, combative and determined team'. His impact was immediate, six clean sheets in his first six games. They'd not managed one in the nine games before he took over. He recorded four wins on the bounce. By the end of his first season, they'd won the Europa League again, beating Athletic Bilbao in Bucharest. His side then battered Chelsea 4-1 in that game in Monaco. A historic Copa del Rey win against Real Madrid in the Bernabeu would follow in May 2013, but this season has the potential to be better than all.
And the main reason is the man in who wears the black suit, shirt and shirt: Diego Simeone.