Murillo is fighting to be fit for their Europa League opener with Real Betis.
He told Sky Sports: "We have an excellent coach, if he wasn't, he wouldn't be here at Nottingham Forest, so we need to implement his ideas as soon as possible and God willing improve and get back to playing our best football.
"We know that he's a winning coach and he's the current champion of the Europa League. I joked with his assistant Sergio (Raimundo) that we're really hoping that he'll become a two-time Europa League champion.
"He's got very good ideas, he's a very intelligent coach, and he has excellent, really hard-working staff. So we're all dedicated to, as soon as possible, get back to playing our best football."
On Postecoglou’s predecessor, Nuno Espirito Santo, Murillo added: "I have tremendous affection for Nuno Espirito Santo, for the relationship we have, for the trust he placed in me.
"It was like a father-son relationship and I will continue having this respect and wishing him the absolute best and I hope our friendship remains for a very long time. I hope we're friends forever."