The Atletico Madrid boss dedicated his side's title triumph to the club's former coach who passed away in February, and believes the late manager was with his side in spirit
Needing just a point at Camp Nou on the final day of the season to claim their 18th Spanish title, Atleti found themselves behind at the break thanks to Alexis Sanchez's brilliant strike.
But Diego Godin's second-half header ensured the visitors claimed the draw they needed in a dramatic second half that also saw a Lionel Mesi effort ruled out for offside.
Former Atleti and Spain coach Aragones passed away in February, and Simeone said he felt as though the ex-Rojiblancos striker were defending along with the team at Camp Nou.
"It's amazing," Simeone said. "You can't explain it. I have to thank the players, the people who trusted us. We've never stopped working and that's why we're here.
"Today is one of the best days in the history of Atleti. To be champions in Barcelona against a team like this, the champions of all in recent years.
"I'm sure Luis Aragones was defending for us in the second half."
Alexis' fine goal gave Barca a half-time lead which would have been enough to see them retain the title, but Simeone says he was quick to keep his players calm at the break.
"At half-time I told them to be relaxed," he said. "In the first half we did well. I knew if we scored, it would cost them. That's what happened. There was an amazing collective effort from everyone."
The Blaugrana supporters were quick to acclaim Atletico's achievement, with Blaugrana fans breaking out in spontaneous applause on the final whistle.
It was an act quickly recognised by Simeone, who in turn waved his thanks before later remarking: "It was one of the nicest things in football. Barca fans, players and coaches showed they have class."
Simeone now turns his attention to next weekend's Champions League final against city rivals Real Madrid, who claimed the Copa del Rey earlier this season.
"I tell the fans we look forward to seeing them all, to see Madrid in red and white," he added. "Today we are making history, but we have to prepare for the final on Saturday."