The Toffees boss says he has the backbone to deal with criticism of him and his team.
After finishing 11th last campaign, the Toffees are suffering another poor season under the Spaniard and currently sit 12th in the table, a full 11 points off a guaranteed Europa League spot.
Saturday's collapse from 2-0 up to lose 3-2 at home to West Ham left the club with just one win in their last eight league matches at Goodison Park since November.
The Merseysiders' inconsistent form has been a source of ire for fans and cause of criticism from the media, but Martinez insists that he has the strength to deal with the ever-increasing scrutiny.
He said, as quoted by the Echo: "I’ve been very fortunate, I’ve had 10 years as a manager and seven in the Premier League and it is a real source of a strong backbone, to have the experiences we have.
"Every situation you are in, in the Premier League, is a high pressure situation. I share the expectations and I am the one bringing the expectations on, it is that we need to understand those expectations because we are Everton.
"We are club that should be winning silverware and putting ourselves in positions to become a winning team. We need to be hand-by-hand and work together to learn how to be a winning team."
Everton host Chelsea in the FA Cup quarter-final at Goodison Park and defeat would not only end any chance of silverware, but would also be likely to all but finish off the club's hopes of qualifying for Europe.
The Toffees' 11th-place finish under Martinez last season was the first time in nearly a decade that the club had ended a season outside of the Premier League top half.