While Everton were losing 4-1 to Arsenal in the FA Cup quarter-finals last weekend, Martinez's team slipped to seventh in the English Premier League following Manchester United's 3-0 win at West Bromwich Albion.
The Toffees are now nine points behind fourth-placed Manchester City with 11 matches left, leaving them facing an uphill task to qualify for Europe's elite club competition. Martinez has won plaudits for his work since replacing David Moyes, who joined Manchester United last summer.
But Everton have lost four of their last seven matches in all competitions since the end of January. Their home form remains strong however, with nine wins and just one defeat from their 13 league matches at Goodison this season.
And Martinez maintains that the top four is still the target, with Arsenal and City's reactions to being knocked out of the Champions League in midweek potentially having a big effect on the run-in. "We have 48 points and that is a good return. Can we get top four? Mathematically we can," Martinez said.
"You look at the points tally you might need to get in those positions and that is still achievable. It would depend as well on how the other clubs react to being - or not being - in Europe. Many aspects are going to affect the points tally needed to be in the top four. After that you have the Europa League to fight for.
"The Europa League wouldn't be a hindrance, not at all. Qualifying for Europe for us would be a massive step forward because it would bring massive football occasions that I feel we need to be able to develop into the type of team we want to be."
Toffee injuries linger
Everton captain Phil Jagielka remains a doubt with a hamstring problem that kept him out of the defeat at Arsenal, while South Africa star Steven Pienaar could also miss out after coming off with a knock in the same game.
Striker Arouna Kone, midfielder Darron Gibson, left-back Bryan Oviedo and on-loan Monaco forward Lacina Traore are all long-term absentees. Having drawn 0-0 at Cardiff in August, Everton have not hosted the south Wales side in the league since 1962, when they won 8-3.
The Bluebirds currently lie in the drop zone in 18th position and have just eight more games to avoid relegation following the visit to Goodison Park. Yet Cardiff striker Craig Bellamy believes he can make a vital difference in the club's fight to beat the drop. Bellamy insists he is ready, and raring to go after overcoming fitness issues in the middle part of the season, to help Ole Gunnar Solskjaer's side in their scrap for survival.
"I sense I'm able to change games whereas at the start of the season maybe I couldn't," Bellamy said. "I've got a better chance of deciding games these days than I did at the start of the season. The way we set up suits me.
"I'm fit, my energy is back, I'm sharp. I'm probably in the best condition I have been in during my time at this club. I'm in a position to do something about my personal performances. I believe we can keep our place in the Premier League. There are still enough points out there against teams we are capable of beating."