When he returned to the club as manager eight years ago, surpassing those unprecedented achievements seemed impossible.
As for on the continent? That was not really to be his concern as Atletico had competed in Europe’s elite competition just eight times in their history.
Simeone’s own words have put his side’s achievements since into perfect perspective. “We must compare ourselves with Sevilla and Valencia," he once said. Yet, under his charge, this club have been able to aim much higher.
“For me, he is the manager who has changed the most the way of one club,” Ander Herrera told the Telegraph. “It’s unbelievable. You see Atletico Madrid before Simeone. It was a completely different club.”
Those who watched Simeone as a footballer will not be shocked to have seen his style of play and philosophy develop. ‘El Cholo’ was a gritty, hard-working midfielder who never shied out of a tackle. To many, he was unpleasant, dirty and aggressive.
Yet, what is more surprising, and applaudable, is how he has transferred his own characteristics to this group and, in particular, channelled those latter aspects into positives, making Atleti a high-pressing machine with one of the best defences in the world.
“What Cholo is doing for this club is historic,” Antoine Griezmann told UEFA. “It reminds me a bit of [Sir Alex] Ferguson and what he did at Manchester United. Hopefully he'll have that career because he deserves it, and he has taken the team where he intended, to the maximum, to among the best teams in the world.”
It’s a comparison that Juanfran has also used, telling Onda Cero: “For him there is no better team than ours. He feels what this club is - why can't he be the Ferguson of Atleti?”
But, as the Old Trafford faithful know all too well, life after such incredible managers leave is not easy.
Simeone may have signed a new contract with Atletico earlier this season, but that won’t stop constant links with a move to Inter – where his captain, Diego Godin, is set for this summer.
Godin is one of several players whose contracts will expire this summer, as are Juanfran and Filipe Luis, all of whom have been mainstays of this incredible team in the most special of eras.
Lucas Hernandez has already agreed a €80 million move to Bayern Munich, the type of big money move that speculation suggests could also arise for the likes of Jan Oblak, Saul and Griezmann.
Atletico are used to losing their prize assets. Sergio Aguero, David de Gea, Diego Forlan and Radamel Falcao are just a few of the names that have passed through over the last few years.
Yet, replacing the backbone of this team is not something that can be done so easily. In fact, the underwhelming arrivals of Thomas Lemar and Gelson Martins have shown that a player needs more than just obvious talent to fit in and be a success under Simeone.
"The players’ positive attitude is what makes us competitive," Simeone explained. "The group accepts that the coach is looking for what the team needs to find the best possible way to win games."
It’s his passion, fight and incredible ability to upset the odds that makes him and his team so likeable, despite typically defensive managers, such as Jose Mourinho, often criticised in today’s game.
"There is not one way of playing football,” Simeone once said, in defence of the Portuguese coach. “You can have ten at the back or ten up front, what matters is the result."
He is the perfect example of that. The Argentine sits at the very top of the list when it comes to Atletico’s most successful managers, and by some distance.
Even when he leaves the Spanish capital, whether that will be in the near or distant future, Simeone’s name will forever be synonymous with the club.
His achievements - which include a La Liga title and two Champions League finals - mean that this weekend’s crucial La Liga title clash pits Barcelona against the ‘other’ side of Madrid, with Simeone’s men able to close the gap to five points with seven games to go.
Whether they can chase down the reigning champions, particularly given Messi's unstoppable form, may be unlikely.
But it is not in this team's nature to give up, with Simeone himself still eyeing the title.
"Competing is in our nature and we want to compete for La Liga until our last breath," he said.
And as his band of brothers are slowly but surely picked apart, causing yet another upset would be some last hurrah for the greatest team in Atletico’s long history.