Reports in Spain have claimed that the 50-year-old could be sacked if results do not improve soon following the team's 4-0 derby defeat to Sevilla on Sunday that left them rooted to the foot of the La Liga table.
"You have to pick yourself up and that goes for everyone, from the coach and technical staff to the fans, we should all be aware that the situation is bad," Football Espana quotes Gordillo as saying. "We must each do our bit and we have to be behind the team.
"The confidence in Mel remains the same, for what is happening at the moment and for what we have experienced together. We continue forward with him as our coach. There is a long way to go in the League.
"We know what faces us, but we have trust in our coach. We give him much credibility. He has to pull things together much like everyone else must."
Gordillo added that Mel will not be sacked even if Betis fail to win against 19th-placed Rayo Vallecano at the weekend.
"Is he playing for his future this weekend? I think it is hasty to say that," he said. "Every game is a final because we have to try win by all means.
"For me he is not playing for his future, of course not. He has demonstrated a lot and we want the team to progress forward with him as soon as possible."
Mel has been in charge of Betis since 2010.