Atleti broke through for their first league title in 18 years in the 2013-14 campaign, stunning perennial challengers Barcelona and Real Madrid, while Simeone's men also went within seconds of winning the UEFA Champions League.
While Atletico's La Liga success was considered one of the fairytale stories of last season across Europe, Simeone, who has been in charge at the Vicente Calderon since December 2011, claimed it had been coming.
The Spanish capital club won the UEFA Europa League in 2010, while Simeone led them to another title in the second-tier continental competition in his first season in charge.
Atletico also won the UEFA Super Cup after each of their Europa League titles, while their 2013 Copa del Rey triumph showed they could match the big boys of Spanish football as they overcame Real in the final.
"Last year was no fluke, it was a consequence of what has been going on at the club," Simeone told AS.
"First it was [winning] the Europa League, then the European Super Cup, Copa del Rey, third in the League and the following year the League title and the Champions League final."
Simeone added that with the additions of - amongst others - Mario Mandzukic, Antoine Griezmann and Jan Oblak, plus the retention of a large chunk of last season's squad, there is no reason Atletico cannot challenge the likes of Real and Barca again.
"The technical department have been working through all of this during the past 40 days," the Argentine said.
"Filipe [Luis] left and [Guilherme] Siqueira came in. [Thibaut] Courtois has gone while [Miguel Angel] Moya and Oblak are now on board; up front we've lost [Diego] Costa and Mandzukic has arrived.
"Griezmann will give us the velocity we've lacked and needed. You don't [create] a team from just 11 players but 18 or 20."
