Atletico pipped both Real Madrid and Barca to the title last year on a dramatic final day, in their first league championship win since 2014.
The club have since strengthened in this summer's transfer market, signing Griezmann on loan from Barca on deadline day -- two years after he made a €120 million switch from the Wanda Metropolitano to Camp Nou -- as well as midfielder Rodrigo de Paul from Udinese and Brazil forward Matheus Cunha from Hertha Berlin.
"We expect to improve on what we did last season," Simeone said in a news conference ahead of Atletico's LaLiga match at Espanyol on Sunday. "We didn't have a good Copa del Rey. We competed well in the Champions League but would like to have done much better. This year we have the Spanish Super Cup in January.
"They're four important competitions including the league, and we want to improve on last season's numbers as we always look to do."
Atletico won LaLiga with 86 points last season, two clear of local rivals Real Madrid and seven ahead of Barcelona.
They were knocked out by Chelsea in the Champions League round of 16, and beaten by minnows Cornella in the Copa del Rey second round.
Simeone said he understood why fans had been angered by Griezmann's controversial departure for Barca in 2019 but expected them to back the France international on his return.
The 30-year-old -- who is Atletico's fifth all-time top scorer after his initial five years at the club -- joined on an initial one-year loan, with an optional second, and Atletico being obliged to make the deal permanent if a set of performance targets are met.
"Griezmann was really keen to come back to Atletico Madrid, he's enthusiastic about returning to the team," Simeone said. "I think Atletico Madrid fans will expect from Griezmann what they expect from us every day, the fans are very demanding and it's normal that they demand the same from Griezmann that they demand from us."
"When you talk about a good or bad squad, you can answer that at the end [of the season]," he said. "At the start it's easy to talk about names but the reality isn't the names, it's the players and what they deliver...