Arsenal need to find the right balance between attack and defence if they are to finish the season successfully, manager Arsene Wenger says.
Wenger saw Pierre-Emerick Aubameyang score a debut goal and Aaron Ramsey his first hat-trick as his side thumped a disorganised Everton.
However, Arsenal have not kept a clean sheet in eight Premier League matches, and finished Saturday's match five points adrift of a Champions League qualification place.
"Our challenge is to find a balance," Wenger said. "We're a very offensive team but need to find a balance between attacking and defending. That will be our challenge until the end of the season."
Allardyce criticises 'pathetic' Everton
Aubameyang, a club-record £56m signing from Borussia Dortmund on Wednesday, chipped in from fellow new arrival Henrikh Mkhitaryan's pass as the home side led 4-0 by half-time.
Television replays showed the goal should have been ruled out for offside, although the visitors could hardly claim the decision made a huge difference to the match.
Everton conceded three times in the opening 20 minutes amid defensive chaos, with Ramsey touching in the opener from Mkhitaryan's cross.
Laurent Koscielny got in front of Aubameyang to head the second at the far post after Shkodran Mustafi glanced on Mesut Ozil's corner, before Ramsey scored a deflected third.
Aubameyang struck the fourth before half-time, prompting Everton manager Sam Allardyce to abandon his three-man central defence and revert to a back four.
Substitute Dominic Calvert-Lewin headed an Everton consolation from Cuco Martina's left-wing delivery, before Ramsey swept in his hat-trick goal from another low Mkhitaryan cross.
Wenger was pleased with Ramsey's showing, saying: "He is calm in finishing. He used to rush it. Over the years, I think he can get 10-15 goals a season."
However, Arsenal lost goalkeeper Petr Cech to a calf injury in a collision with Oumar Niasse as the striker hit the post in the second half.
In normal circumstances, Ramsey's hat-trick would have guaranteed him the headlines, but Aubameyang's high-profile arrival during the week ensured he grabbed the attention.
The Gabon striker did much to lift the mood among fans despondent after Tuesday's 3-1 defeat at Swansea.
Aubameyang overcame a midweek illness to start against Everton - and his first display in Arsenal red was perhaps a sign of things to come.
There was a well taken goal, although it should not have counted, and a demonstration of his fearsome pace. In one first-half break he raced clear on to an Ozil pass and he was denied only by the knees of Everton goalkeeper Jordan Pickford.
On the flip side, there was also a hint of his individualistic streak - he did not seem too thrilled when Koscielny beat him to the scoring touch for Arsenal's second, throwing his arms out in front of him in an apparent gesture of mild frustration.
He can drift out of games too. He touched the ball 25 times during the match. No outfield player who started the game had fewer touches.
However, if he can produce the kind of scoring form that marked his time at Dortmund - where he worked well with Mkhitaryan - Arsenal may yet reach the top four.
"It is very early, but they look to have the quality to integrate into the game we want to play," Wenger said. "They are quick, have sharp movement and are agile and want the ball. It is very good and positive signs."
Three is not the magic number
Sam Allardyce's 500th game as a Premier League manager was ruined as a decision to start with a three-man central defence backfired spectacularly.
His Everton side lacked defensive discipline as they made only three tackles in the first half, while players were frequently caught out of position.
Allardyce's plan appeared to be to shut out the home side centrally while using Jonjoe Kenny and Cuco Martina as attacking wing-backs.
It would have been a big enough test for a defensive line-up used to playing together. In a line-up containing one debutant - Eliaquim Mangala - and two other defensive changes from the previous game, it was a recipe for calamity.