Everton were beaten 2-1 by Manchester United in the FA Cup semi-final.
The Toffees were beaten 4-0 by Liverpool earlier in the week, and they were then knocked out of the FA Cup by Manchester United yesterday.
Everton had performed well throughout the contest at Wembley, but they were undone in the last minute when Anthony Martial raced through on goal and finished well.
It was a heartbreaking way for Everton to lose the FA Cup semi-final, and Martinez says that in such situations it can be hard for supporters to reflect positively.
“I have spent three years at the football club and I’ve always said Everton is a very special club,” he said. “You could see that with the way the fans represented the football club at Wembley.
“Every season we are developing and we are reaching certain signs that we can please our fans and bring silverware that they deserve but clearly in moments like this - of true disappointment - it can be real difficult to see the good things we have developed.”
Sections of Everton supporters were already calling for Martinez to lose his job before the defeats against United and Liverpool.
The Spanish boss’s job is now looking very insecure, though, after a season which can only be considered a disappointment.
Everton may have reached two cup semi-finals, but they are stuck in 11th place in the Premier League table, and that position does not reflect the quality that is in the squad at Goodison Park.