A 4-1 defeat in the quarter-final at the Emirates Stadium left the Toffees facing a fight to secure European football in the last two months of the season.
They have slipped behind Manchester United into seventh but do have a match in hand and Martinez wants to see his side show their character from now until the end of the campaign.
"If you don't get hurt by that (Arsenal defeat) you have got nowhere to go really if you don't have those feelings," said the manager.
"We are fully focused now. We have just got the league - 33 points to play for, which is a phenomenal amount.
"The season now is very much alive for us. As a group now we have got a clear indication of where we need to get."
Everton have run the top sides close in many of their encounters this season and Martinez believes that has given his players encouragement moving forward.
"If anything that is going to give even more motivation and a bigger incentive to beat those margins," he added.
"I think at the beginning of the season you get those teams who are expected to win titles because of the financial approach.
"We are in a position where, because of our football club and the history we have, we should be expecting to win titles.
"It is going to be a bit of a process and a bit work but I think you saw we are not far away from being able to go to Arsenal and be able to get through to an FA Cup semi-final.
"Now it's just a matter of making sure the small margins get affected in our favour and we can progress without expecting to go into big places like the Emirates and be beaten.
"The performances are showing that we're starting to develop that belief so the next stage is to be able to reflect it in the scoreline."