It left the Toffees chasing Manchester United and Tottenham in the pursuit of a Europa League place but Martinez is a firm believer in taking positives from every situation and expects his side to grow after losing at the Emirates Stadium.
"We want to get into a position where we can learn from these sort of games to control the small margins but all the focus and concentration goes into the league, there is no reason for distraction," said the manager.
"It has been an intense period; we lost to Arsenal away from home and they have been involved in Champions League football for many seasons.
"It was a game which could have gone either way but there is no shame in losing a quarter-final away from home against a team like Arsenal.
"When you work together you develop many aspects in your performance and we have been developing and getting stronger.
"From the disappointment of going out of the quarter-finals of the FA Cup you learn what you can do better and develop experience.
"We have an incredible opportunity to be as good as we can for the fight of the final 11 games of the season and that is where everything gets decided.
"We've had a good campaign so far which has given us a solid amount of points and now we need to make sure we fight for every point and make sure we are a strong team until the end of the season."
Goalkeeper Tim Howard, rested for the FA Cup, returns to face struggling Cardiff at Goodison Park on Saturday but Martinez admits at this stage of the season he is keeping an eye on his players' overall fitness.
"We need to be fresh
You get into this part of the season where players are starting to accumulate close to 3,000 minutes and you need to be a little aware of certain positions on the pitch," he explained.
"The squad is ready and we can cope with just sharing the demands of the next 11 games.
"Gerard Deulofeu and Aiden McGeady are fully fit and ready to finish the season strongly."
Everton captain Phil Jagielka faces a late fitness test on a hamstring injury.
Centre-back Ben Turner could be doubtful for relegation-threatened Cardiff
The 25-year-old suffered a knock late in the Bluebirds' vital win over Fulham last weekend
Spanish defender Juan Cala is back in contention after recovering from a stomach bug.
Manager Ole Gunnar Solskjaer will take inspiration from his opposite number Martinez as he continues his attempt to engineer top-flight survival.
Martinez steered Wigan away from the drop in the latter stages of three successive seasons after taking over at the DW Stadium in 2009.
He was unable to repeat that feat last year, as Wigan finally succumbed, but he did oversee their remarkable FA Cup triumph.
Solskjaer knows his team need to replicate some of Martinez's Wigan magic to pull out of and away from the relegation zone with just nine Barclays Premier League games remaining.
The Norwegian said: "If we can get on the same kind of run we will stay in the Premier League.
"It will take everything we have got to get where we want
That will give us the reward we all crave - playing in the Premier League.
"It is a vital period
We believe, we hope that we have turned a corner in terms of belief and performances
We are still in with a shout."
Source : PA
Source: PA