The Spanish outfit challenged for a top-four place for a large part of last season but they currently sit in the relegation zone, having collected just eight points from their 10 matches in the new campaign.
"Every day I have woken up with a new problem since I have been here, but Betis have been growing," Mel told reporters at a press conference. "It is not possible to be satisfied and I believe that is not fair and I believe the Betis fans deserve to hear from their coach's mouth why I am here.
"I do not want days to pass before we get to the game against Levante. Last night was tough for me, not for the result but for a number of reasons. I'm at a club where it cost me much to get here."
"I worked hard to be here, and I want to continue working and rewarding the fans who have never let us down. I cannot jump ship. I would be a coward, I would be a bad professional. Now I have to work harder still."
Betis have won just twice in the league this season.