Burgos has been Simeone's number two since the Argentine arrived at the Vicente Calderon in 2011, and has been a constant presence on the touchline over the last couple of seasons.
The 48-year-old, who was a goalkeeper during his playing career, has said that his relationship with Simeone is successful because they are both "very strong characters".
"If one of us loses our temper, the other will put up with it until it fizzles out," Burgos told Papel. "You know, both of us have very strong characters, but my job is to make sure he remains balanced. If he has any doubts or anxieties, I try to free him of them. I'm never in any doubt, never.
"When you are presented with the truth, there is no need to doubt and my role is to tell him the truth always - this one can play, he can play and he can play and he trusts my judgement. The roles of coaches and their assistants is a bit like those double acts in classic films - like Robert De Niro and Joe Pesci."
Atletico will welcome Real Madrid to the Vicente Calderon on Wednesday night looking to overcome a 3-0 first-leg defeat in the semi-finals of the Champions League.