The Blues boss is under increasing pressure following another disappointing campaign.
The Blues have endured another disappointing campaign this season, currently sitting 14th in the table and unlikely to finish in the top half.
The one saving grace has been their form in the cups, with the reaching the semi finals of both the League Cup and the FA Cup so far.
Manager Roberto Martinez has found himself under increasing pressure at Goodison Park as a result, and Mills says winning the latter could be the only salvation in keeping his job next season.
“Everton winning the trophy would veil some of the problems at Everton,” he told Sportlobster.
“It could be vital to Martinez’s relationship with the owners and may be his only salvation in keeping his job into next season. Everton have a great deal of quality in that squad.”
“For me, the undoing of Roberto Martinez is his inability or unwillingness to field a side who can close a game out. They’ve lost far too many points from leading situations this season and it’s cost them.”
The problem for Everton is that they have arguably drawn the hardest of the last four ties this season.
They are set to face either Manchester United or West Ham once their quarter-final replay is settled this week.
Neither of those are the opponents the Blues would have ideally wanted given they are both competing for a top four place this season, meaning Martinez may be facing further scrutiny in future.