The Toffees lost 4-0 to Liverpool and the margin of the result could have been far higher had the Reds not treated the final 15 minutes like a training game.
Martinez is in his third season with the Toffees and Merson believes his spell at the club could soon be all over.
Everton face Manchester United at Wembley in the FA Cup this weekend in the semi-final, and Merson predicts it is a game the Red Devils will win 2-1.
He said: "I don't see how Roberto Martinez can last if he loses at Wembley. He has got things horribly wrong this week.
"He should have played his strongest team and won against Southampton and then told fans he had to rest everyone against Liverpool in preparation for the semi-final.
"Instead he rested everyone against Southampton and got booed off and then played his best team against Liverpool and got battered.
"For the first time he looked lost on the sidelines, the fans have turned and I don't see how he can hold on if they lose. I felt sorry for him but it's a situation of his own making, this is a good team that is nowhere."
Even if Everton do win, Martinez may only be buying himself time. Failure to win the final against either of Watford or Crystal Palace would seem like an even bigger failure than a semi-final loss to United, and their league position of 11th place does not lie.