Diego Simeone masterminded a first league championship in 18 years last season as Atletico edged out Real Madrid and Barcelona, but they have only defended the crown twice in their history.
To try to repeat the feat they last achieved in 1950-51, Atletico have added Mario Mandzukic, Jan Oblak and Antoine Griezmann to their squad, but have also seen important players such as Diego Costa, Filipe Luis and David Villa depart.
Real and Barca have far greater resources at their disposal and have both spent big in the close-season, with Ivan Rakitic and Luis Suarez moving to Camp Nou, while the European champions have acquired the services of James Rodriguez and World Cup winner Toni Kroos.
Those signings have left Atletico captain Gabi in little doubt as to the size of the challenge Simeone's men face.
"It will be difficult to repeat what we did last year because Barcelona and Real Madrid have much bigger budgets than we have," he told AS. "They spend more than we can in new signings and they both have great squads.
"We will try to compensate for that with effort and ambition.
"Winning the double will be difficult although we will never give in, or rule anything out."
Atletico begin their season against Real in the Super Cup before starting their league campaign against Rayo Vallecano on August 23.