Boss Carlo Ancelotti admits Everton face a battle to reach Europe and may need to win their final three games of the Premier League season to qualify.
The Toffees missed the chance to move level on points with fifth after a dull goalless draw at Aston Villa.
Emi Martinez thwarted Ben Godfrey and Dominic Calvert-Lewin but, aside from late pressure, Everton rarely looked like claiming victory.
Neither did Villa but they at least welcomed back Jack Grealish from his three-month absence with a shin problem.
Everton climbed to eighth in the table but Ancelotti knows they are up against it to reach Europe.
He said: “We have three games, maybe we have to have three victories to be in Europe and we will try to do it.
“We played two away games, we got four points and it would be better to have six points but four points is good to stay in the fight.
“It’s a point, we moved up the table and now we have a great opportunity at home.
“The game was a good game, a good performance, we were much better in the second half where we put more pressure offensively and created chances.
“We could have won – we didn’t but nothing changed our idea to fight to the end of the season.
“We could have been more efficient to finalise the shot or final pass but the strikers worked really hard defensively.”
Tyrone Mings headed Villa’s best chance wide after 17 minutes of a forgettable first half and, while Everton improved after the break, they struggled to find top gear.
Martinez denied a stretching Godfrey at the far post while Andre Gomes wasted several fine openings on the edge of the box.
Jordan Pickford saved Anwar El Ghazi’s free-kick but the game failed to come to life until Everton finally lifted themselves in the closing minutes.
Calvert-Lewin’s header was saved by Martinez with Abdoulaye Doucoure and Richarlison failing to convert the loose ball while Allan also fired over in stoppage time.
Villa remain 11th but boss Dean Smith was pleased to see skipper Grealish return for the first time since February.
He said: “I’ll sit down with him and see how he feels but he brought a spark onto the pitch straight away.
“It wasn’t quite happening in the final third, he had one mesmerising run when he had five or six Everton players chasing him.
“We’re really happy to have him back, it’s small steps at the moment but it’s great to have him out there. It was a strange injury but he’s come back now, he looks fresh and we need to go softly, softly with him.
“It was a game of few chances. We had good control of the ball in the first half. The game was lacking that bit of spark in the final third.
“They were chasing the game at the end as they are trying to get into the European positions. We had to defend resolutely.”
