Arsenal boss Arsene Wenger admits his side's resident status in the Champions League is under threat after a 3-0 defeat at fifth-placed Everton.
The Gunners are one point ahead of the Toffees having played a game more.
"I'm 100% determined to fight to make the top four but it will be difficult," said Wenger, who has led his side to 16 successive top-four finishes.
"We have a [run-in] that is feasible but we must focus on the quality of our displays before dreaming of places."
Arsenal, who were beaten 5-1 by Liverpool in February, suffered again on Merseyside as strikes from Steven Naismith, Romelu Lukaku and an own goal by former Toffees midfielder Mikel Arteta gave Roberto Martinez's side a comfortable victory.
It was a first win for Everton over Arsenal in 15 attempts and Toffees boss Martinez said that an "arrogant" performance at Goodison Park had kept his Champions League "dream" on course.
But he warned his side would need to be "perfect" during their final six matches.
With one more game to play than the Gunners, Everton's destiny is in their own hands - but they have to play both Manchester City and Manchester United at Goodison Park.
"In terms of the satisfaction you can get as a manager, it is as good as it gets," the Spaniard said of his team's display.
"The players in every area were phenomenal. It was a huge three points from a psychological point of view.
"I always like to have a dream to follow. When it was Swansea it was to get into the Premier League, at Wigan it was to get into Europe and at club with the heritage of Everton it is to get into the Champions League.
"There is still a long, long way to go. Arsenal now have 15 points to fight for and it is going to be a really tough battle."
After another miserable result, Wenger confessed that his side had lost their "charisma" following another disappointing away performance against their leading four rivals this season.
But while Everton face a difficult run-in, the highest ranked of Arsenal's remaining opponents are ninth-placed Newcastle.
"The fight [for the top four] is very open and not only dependent on us," Wenger added.
"Everton are in a strong position. We have been confronted by that before and it is down to how we respond to such a disappointing performance.
"It is a massive worry to lose a game like that. We need to go back to basics.
"I wouldn't question the spirit of the team - they are focused and want to do well, they have just lost something on the confidence front.
"It is difficult to identify if it is fear. The heavy defeats away from home have taken some of our charisma away. Is that fear, is that belief, is that confidence? Maybe a bit all together."