The Vicente Calderon side finished three points clear of both traditional Spanish giants last season, winning their first league title for 18 years and even reached the Champions League final.
Simeone, though, fears it might be too much to ask a repeat of that success following the arrival of Luis Suarez and Ivan Rakitic at Barca and that of Toni Kroos and James Rodriguez at Madrid.
"Atletico are not like Barcelona and Real Madrid. They have a structure that allows them to spend €80 million (£70m) on one player, while we have spent about €100m (£80m) in total," Simeone told La Gazzetta dello Sport.
"Lionel Messi, Luis Suarez and Neymar are three of the five best players in the world. Barcelona signed Suarez and Ivan Rakitic, while selling Alexis Sanchez and Cesc Fabregas. They have improved.
"And then there's Madrid. They signed Toni Kroos and James Rodriguez, while Gareth Bale will be even stronger than last season. They are better than last year, too, and quite a bit...
"It will be hard for us to compete with them. It's easy to understand that people wonder whether we can repeat last year's success. We should remember that it had been 18 years since the last title. What happened last term was something special.
"Atletico are champions, but the players aren't the same. We're in a different league than Madrid and Barca."
Atleti start the new Liga season away against Rayo Vallecano on Monday.