Everton face two hugely important matches in the coming days.
Everton fans have grown very frustrated this season, with the calls for Martinez to be sacked growing louder by the match.
The Toffees have badly underperformed, but they now face a season-defining week.
Everton face Liverpool on Wednesday night, before they take on Manchester United in the FA Cup semi-final at Wembley at the weekend.
And Martinez said: “The message is very clear. We understand that nobody can be happy with the results we have had a home. But we are giving everything we have got try and replicate the away from into our home form. And then, we need our fans to do as well as we can in the FA Cup.
“Everything we do is to make our fans proud, but without them we cannot achieve our best level.”
Martinez has suggested that Everton will not allow the prospect of an FA Cup semi-final to distract them from the task at hand in the Merseyside derby.
The Spanish boss has said that he intends to pick a strong line-up against Liverpool, as he looks to ensure his team do not suffer another damaging home defeat.
Everton then can concentrate on United, as they look to make it into the final of the FA Cup.
The Toffees have already fallen short in the League Cup semi-final this season, and they will be determined to avoid a repeat scenario this time around.