Simeone picked up an eight-game suspension after being sent to the stands during Atletico's Supercopa second leg against Real Madrid last week and reacting by tapping the fourth official on the head.
The first match of the coach's ban saw defending Liga champions Atletico - who have still not been officially presented with the league trophy - stutter to an unconvincing 0-0 draw at Madrid neighbours Rayo Vallecano on Monday.
Simeone's assistant and former Argentina team-mate Burgos took charge at the Estadio Vallecas and he will do so again as newly promoted Eibar head to the Vicente Calderon on Saturday.
Although Atletico find themselves playing catch-up on title favourites Barcelona and Real Madrid after just one game, Saul does not feel Burgos being in charge represents a disadvantage.
"He always spreads everything he has to us; his winning spirit, confidence," the 19-year-old said.
"Of course, you can see that. German is doing immense work.
"It is very difficult to suddenly have this punishment [Simeone's ban] and [for Burgos to] have to play this role, but we know that he is prepared for it."
Eibar go into the fixture on the back of winning their first ever top-flight fixture after beating Real Sociedad 1-0 on Saturday.
Atletico will be hoping to kick-start their campaign against the Basque side, particularly with both Real and Barca facing potentially tricky trips following their wins on matchday one.
Luis Enrique's Barca head to Villarreal on Sunday and they will be aiming to produce a more convincing performance at El Madrigal than they did last term.
After falling 2-0 down, Barca – who were then coached by Gerardo Martino – had to rely on three goals in the final 25 minutes to snatch victory.
Real make the trip to San Sebastian on Sunday to face Real Sociedad and they will be looking to continue their excellent recent run against the side of under-pressure Jagoba Arrasate.
Last term Carlo Ancelotti's side accumulated a 9-1 scoreline against Sociedad over the course of the two league meetings.
Europa League champions Sevilla travel to Barcelona on Saturday as both they and Espanyol hope to move past opening-day draws, while Athletic Bilbao host Levante just three days after their Champions League play-off win against Napoli.
The other two newcomers Cordoba and Deportivo La Coruna have home games to look forward to, with Celta Vigo and Rayo their respective visitors.
In Friday's matches, Malaga face the tough task of leaving Valencia with a result, while Getafe welcome Almeria to Coliseum Alfonso Perez and the weekend finishes with Granada's trip to Elche.