Martinez's men find themselves dangerously close to the drop zone - just six points clear of third-bottom QPR - after four league matches without a win.
Everton, who were swept aside by Arsenal on Sunday, are back in action on Wednesday as they travel to Stoke City and Martinez said it is time for the club to stick together.
"I understand completely where we are and I'm very much conscious that this is a moment that we need to grab with both hands and face it as a football club," Martinez said.
"We rely on our fans and if we get together and help our players in the 90 minutes then we are going to get the benefits long-term, not just for this season.
"It is the talent and attitude that gives me the feeling of satisfaction with the squad.
"Now, it is about making sure the day to day brings results and now is the time we need to stick together because we will get the benefits going forward."
