The Spain striker felt the capital club deserved to land La Liga for its fighting spirit and the brilliance of its coach.
Atleti got the point it required with a 1-1 draw at Barcelona, with Diego Godin's header enough to deny the home side the win which would have seen it defend the title based on head-to-head record.
It is a remarkable achievement for Atletico, which has a budget the fraction of those enjoyed by Barca and Real Madrid, and Villa believes a great work ethic – and the brilliance of Simeone – proved vital.
"Cholo [Simeone] is everything here. He is the courage, he is the reflection. With his knowledge and a lot of warriors, we have achieved," he told Canal Plus. "I'm very happy to have put the icing on this successful season."
Atleti's hopes hung in the balance after Alexis Sanchez put Barca in front after 34 minutes until Godin’s towering header at the start of the second half proved enough for the visitors.
"This match was a reflection of the year. We gave all we had. We had everything against us today, with two injuries [to Diego Costa and Arda Turan], but we learned how to react," ex-Barca striker Villa added. "We have been better than our rivals in the Liga. The last 10 minutes of the first half showed this. Another team, against Barcelona, in their stadium would have collapsed, but not us."
Next up for Atletico is the Champions League final against city rivals Real in a week’s time.
"We have to celebrate this Liga title, there is time to prepare for the final. There is still the desire to keep going," Villa said.