Arsenal manager Arsene Wenger admitted the race for the final Champions League place has been blown wide open after his side's 3-0 loss away to Everton at Goodison Park on Sunday.
The gap between Arsenal in fourth place in the Premier League and Everton in fifth spot is now just a point, and the Toffees have the advantage of a game in hand on Wenger's side.
Arsenal have qualified for the Champions League for the past 16 consecutive seasons, a qualification record for the competition bettered only by Real Madrid and Manchester United.
Everton now have the opportunity to break that streak although Wenger claimed his players would draw upon the experience of previous seasons to secure fourth spot and with it a place in Europe's premier club competition next season.
"The fight is very open and is depending not only on us," Wenger said. "Everton are in a strong position but we have been confronted with that before and it is how we respond.
"I am absolutely 100 percent determined to fight for the top four, it will be difficult," the Frenchman, the longest-serving manager now in the Premier League, added.
"We have a programme of fixtures that is feasible, but we must focus on the quality of performances before we talk about that," added Wenger, who will expect a much improved effort from Arsenal in their FA Cup semi-final with holders Wigan at Wembley on Saturday.
"Our performance here was not convincing or defensively or offensively. It's disappointing a result and performance. The two go together and now we have to regroup and go back to basics," said the Gunners manager.
Everton secured victory after a stirring display in which Arsenal only sporadically tested goalkeeper Tim Howard.
- 'Phenomenal Everton' -
Steven Naismith gave the Toffees the lead when he stroked the ball home in the 14th minute after Romelu Lukaku's shot had been parried by Wojciech Szczesny in the Arsenal goal.
Everton doubled their lead just after the half-hour mark when on-loan Chelsea striker Lukaku notched his 12th Premier League goal of the season.
The Belgium international received a cross-field pass on the right flank and skipped past Arsenal defenders Nacho Monreal and Thomas Vermaelen before he struck a powerful shot into the corner.
Former Everton midfielder Mikel Arteta put through his own net in the second half to seal the points for the Toffees.
Everton manager Roberto Martinez said this win had seen his side overcome an important mental hurdle.
"The implications today (Sunday) were quite unique," Martinez said.
"We were hoping for a result but what was needed was breaking many barriers -- 22 games we played against Arsenal, we only scored one goal or less.
"We kept a clean sheet and scored three and looked like we could have scored more. It was a huge three points from psychological point of view," the Spaniard added.
"We knew if we could get the three points it would leave us with 63 points which is an incredible amount but we still have 18 points to play for."
Martinez refused get carried away with his side's top four prospects with six games of the season remaining, although he acknowledged the team had the confidence to aim high.
"The players in every area were phenomenal," said Martinez. "The tactical awareness, work rate, the discipline. In a group sport it is as good a performance as it gets in that from that point of view.
"It's not going to be straightforward to qualify for the Champions League but the mentality of the group is that we believe in ourselves and can do it."