The Toffees drew 1-1 at Watford on Saturday afternoon.
During Saturday's 1-1 draw at Watford, a section of the visiting fans unveiled a large blue banner which read 'Martinez out' - a symbol of the worsening relationship between him and the supporters after he forced Leighton Baines to apologise for comments relating to the Toffees' lack of chemistry during the week.
The former Wigan boss has not helped his cause by the fact that his troops appear to be labouring big time in the Premier League, with the draw at Vicarage Road meaning that they have won once in their last six top-flight outings - a 3-1 win at bottom-of-the-table Aston Villa.
Asked if growing frustration from the terraces affected his side, Martinez responded: “No, it is the opposite. We share that feeling," he's quoted as saying by Team Talk. “The fans are allowed to express their views, and once the game started the support was magnificent. For me they are the best fans in world football.”
Martinez's only saving grace this season might be the fact that they remain in the FA Cup, and will prepare for a semi-final bout with either West Ham United or Manchester United at Wembley in the coming weeks.
Elimination from that might well spell the beginning of the end for Martinez, who replaced David Moyes in 2013.