The Sicilians, who recorded an impressive eighth-place finish in Serie A last term, lost 2-1 at Fiorentina before falling 3-0 to Inter Milan.
"The game against Inter was the worst performance by my team since I took over," Maran admitted. "Fortunately, we had the international break to help us work on our mistakes and improve our physical condition.
"I can already see that we are making improvements.
"I expect a different Catania in Leghorn."
Catania midfielder Tiberio Guarente is also confident positive results will come their way soon.
Guarente joined Catania on loan from Sevilla this summer.
"The new signings and I are adapting well to the team," he said.
"We will need time to be perfect but playing like Catania knows how, this team will be able to do well."
Livorno, meanwhile, will have to play the waiting game to see new signing Miguel Borja make his Serie A debut.
The Colombian striker has yet to receive his work permit to play in Italy and will not feature this weekend.
The Amaranto, who returned to Italy's top flight this season, hope to have Borja available in time for next weekend's encounter at Genoa.
In the meantime, Livorno coach Davide Nicola hopes his side can pick up where it left off in its 4-1 triumph at Sassuolo in the last round.
"We played a great game at Sassuolo, a team we knew well from last season," Nicola said. "This triumph proves that we can be a competitive group."
The visitors will be without defender Giuseppe Bellusci and midffielder Mario Izco, both out injured.