There was little quality on show from the home side, with Arsenal superior throughout despite their midweek Champions League exertions.
It has left Everton 12th in the Premier League – and Martinez made no excuses for his players.
He told reporters: “You cannot expect to win a football game with a performance like that.
“We were very fearful. We were waiting for things to happen, we were reacting to things, we never got three or four passes together, we never defended with intensity well enough.
“We looked like a team that played on Wednesday rather than he other way around. Arsenal were sharp, they had a really good intent.”
Martinez added: “To see the contrasting performance from seven days ago is quite hurtful.
“When you see we were not anywhere near our level it is very, very disappointing and clearly shows we need to learn how to play at home in the league.
“We need to learn how to have a real intensity in our play because in the competitions we have that, when we play away we have that, but probably at home we have a bit of fear.
“We want to win so much for our fans that it affects our performances and that is really disappointing.”