Needing just a point at Camp Nou on the final day of the season to claim their 18th La Liga title, Atletico found themselves behind at the break.
Alexis Sanchez fired the Catalan giants in front in the 34th minute after Atletico had earlier lost star striker Diego Costa and midfielder Arda Turan to hamstring and pelvis injuries respectively.
But Diego Godin's second-half header ensured the visitors claimed the draw they needed in a dramatic second half that also saw Lionel Messi have a goal ruled out for offside.
"It's amazing," Simeone said. "You can't explain it. Thanks to the players.
"We've never stopped working and that's why we're here.
"Today is one of the best days in the history of Atleti.
"I'm sure (former coach) Luis Aragones (who passed away earlier this year) was defending for us in the second half."
Goalscorer Godin revealed that his side were inspired by words of wisdom from Simeone at the break.
"We've fought all year and done an amazing job," Godin said.
"To hold off Real Madrid and Barcelona has been difficult.
"Simeone told us at half-time that we were definitely going to score and justice was done."
