Simeone has transformed Atletico into one of Europe's best sides since arriving at the club in 2011, pulling off what many thought was impossible when they won the La Liga title in 2014.
The club have also reached the Champions League final twice and won the Europa League twice under Simeone's leadership, most recently last season when they defeated Marseille in the final.
The Argentine manager's comments came in an interview with Spanish outlet Marca, where he said: "Winning the League competing with Real Madrid and Barcelona is almost impossible, in this last decade, they have had tremendous strength and have had incredible players, but with hard work, continuity and perseverance we got it, too."
Simeone also spoke of his admiration for the players he had seen develop at Atletico during his time as manager, saying: "The best thing is to improve your players, of course we all want to be champions, but the best title is to see players like Koke, Lucas or Correa are growing.
"We do not have the options of the super-powerful teams to spend €150m or €200m on a player, at Atleti we have to be creative to improve the team and what we have to develop."
Simeone's comments suggested overall that the manager is completely settled at the club and has no immediate plans to leave, having recently been linked with a range of jobs such as the managerial position at Arsenal vacated by Arsene Wenger.
"The season that we won the Europa League at Fulham had a very strong connection between the people and the players. It was the beginning of a new cycle, from the beginning, we knew what we wanted," Simeone added.
Atletico's first game of the season is against rivals Real Madrid in the UEFA Super Cup on 15 August.