That last-gasp Wembley loss came on the back of a 4-0 derby defeat to Liverpool and Everton find themselves 11th in the Barclays Premier League, 10 points above the relegation zone and a whopping 23 from the top four.
Given the talent in the Everton squad it is a situation which has led to supporters displaying banners at recent games calling for Martinez to be sacked – and Gray feels that the Spaniard is fast running out of time.
“Martinez is on the brink, there is no doubt about that,” Gray wrote on Sport360.com.
“He has lost most of the fans who would now like to see him go.
“Everyone keeps telling me that this is the best group of players they have had since my day in the eighties when Everton were winning things.
“Well, let me tell you, if that’s true and if they have got the talent – which for me they clearly have – then it’s up to the coach to bring out the best in them and get them playing in a way that brings success and he has failed to do that.
“They have won only four home league games this season and with this group of players that is just not good enough.”
Gray made a damning attack on Martinez’s handling of elegant England defender Stones, who has been criticised for failing to learn from his mistakes.
Everton, who declined to comment on Gray’s remarks, turned down bids from Chelsea last summer to sign the 21-year-old.
But Stones was left out of the team following the Capital One Cup semi-final defeat to Manchester City at the end of January and did not start again for over a month.
“I think he has lost John Stones because of the way he has treated him this season and maybe one or two other players,” claimed Gray.
“What we are seeing is what we saw when Roberto was Wigan’s manager – an entertaining coach who can’t win enough football matches.
“In my opinion Everton have gone backwards since last year.
“Martinez has admitted that he never sends his team out to keep a clean sheet. You are not going to win many games doing that.
“They don’t work hard enough defensively and they get turned over far too easily.
“They have lost more points from a winning position than any other team in the league and that’s unacceptable.
“I have no doubt that this team should be in the top six but they are a million miles away.
“At the end of the season the powers that be at Everton need to sit down and decide whether what Martinez has done in the last three years is progress and, for me, the answer has to be no.”