The Argentine guided the club to their first league title since 1996 last season, as Barcelona were forced to settle for second place and Real Madrid finished third.
A UEFA Champions League final appearance followed, but after the defeat to city rivals Real in Lisbon the break-up of Simeone's team began.
Diego Costa and Filipe Luis both signed for Chelsea, Thibaut Courtois returned to Stamford Bridge following his second season on loan with Atletico, while David Villa left for New York City and Adrian Lopez joined Porto.
Although Simeone has brought in the likes of Mario Mandzukic, Antoine Griezmann and Jan Oblak, the coach does not expect his team to contest the title once again after Real and Barcelona spent big in the transfer market ahead of the new season.
"I don't like to lie to people and one thing is clear: we cannot compete with Real and Barcelona," he is quoted as saying by Gazzetta dello Sport. "Atletico are champions but the players aren't the same. We're in a different league than Madrid and Barca.
"Our rivals are Sevilla, Valencia and Athletic [Bilbao], and the goal is third place. We're a new team.
"The spending on arrivals is due to the players that have been sold.
"We have changed especially in attack. I see it as a new beginning because the team is different: Mandzukic, [Raul] Jimenez and Griezmann are different from Costa, Villa and Adrian.
"We will maintain a solid structure that supports the team, but we're trying to figure out what style suits us best."
Atletico face Real in the second leg of the Supercopa de Espana at Vicente Calderon on Friday, after drawing the first leg 1-1 at Santiago Bernabeu, before starting their league campaign against Rayo Vallecano on Monday.
