“There is no replacement for hard work,” said the Argentine. “The team has understood that, done the work and today is one of the most important days in the history of Atletico Madrid."
Needing just a point to become the first side other than Barcelona and Real Madrid to win the league in 10 years, Atletico fell behind just after the half hour mark to Alexis Sanchez's wonder strike.
However, they responded like champions after the break as Diego Godin powered home Gabi's corner.
There could even be more glory to come for Atletico as they will attempt to win the Champions League for the first time in their history next weekend when they take on Real Madrid in Lisbon.
"We are desperate to get back to Madrid and see the city dressed in red and white. Today we were able to make history, but we need to prepare for Saturday."
Simeone also paid tribute to former Spain manager and Atletico's greatest ever player Luis Aragones, who passed away at the age of 75 earlier this year.
Atletico captain Gabi also hailed the belief his side had throughout the campaign to overcome the riches of Barca and Real.
"The team deserved this title. They have been up to the task. We always believed in ourselves, even when we went behind, we believed in the team and got the draw we deserved.
"It is an honour to belong to this team and to fight with the biggest sides. For now, we celebrate, and from Monday we will start to think about the Champions League final."
Martino resigns after a year of failure
Barcelona coach Gerardo Martino announced he will leave the club after failing to win a major title in his one season in charge.
"I wanted to announce that I have reached an agreement with the club to no longer be the coach of Barcelona," he said at his post-match press conference after the draw with Atletico.
"I would like to thank everyone at the club for believing in me. I am sorry that we didn't achieve the objectives that the club normally does.
"We have tried until the end with a lot of dignity, but in the end we came up against an opponent that was better than us.
Meanwhile, former Barca captain Luis Enrique is expected to be named as Martino's successor after announcing on Friday that he will leave Celta Vigo at the end of the season.
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