Emery’s side extended their winning run to four matches in all competitions with a 4-2 victory over Vorskla Poltava in the Europa League on Thursday.
The Gunners raced into a four-goal lead through Pierre-Emerick Aubameyang’s double and strikes from Danny Welbeck and Mesut Ozil.
But Emery was furious that Arsenal switched off in the closing stages to allow minnows Vorskla to score twice.
It was the latest in a long line of defensive disappointments for Arsenal, who have failed to keep a clean sheet in any of Emery’s six matches in charge.
Arsenal have endured difficulties at the back for years as Emery’s predecessor Arsene Wenger struggled to find the right players to man his defence.
Emery has made changes of his own, giving a debut to goalkeeper Bernd Leno in midweek in place of Petr Cech, while central defender Sokratis Papastathopoulos arrived in pre-season from Borussia Dortmund.
So far that quick-fix plan hasn’t worked, so Emery has called on his team to show some steel and learn from their mistakes.
“It’s our disappointment. Little by little, we are conceding a few chances to the opposition, the same like in Newcastle,” Emery said.
“But we need to continue to improve on this because in the last minute in Newcastle and again today in the last 20 minutes, we conceded two goals.
“Our challenge is to be competitive for 90 minutes of each match and this is one thing to improve.”
Emery made eight changes for the Europa League clash as he rested his key players for Everton’s visit to the Emirates Stadium.
But the Spaniard doesn’t believe that should be used as an excuse for Arsenal’s fragile defending.
“We are speaking before each match to take a mentality of ‘don’t concede chances easily’,” he added.
“I think today is a good opportunity for not accepting goals, but the last 30 minutes, we needed to be better on this competitive aspect.”
Leno, a close-season signing from Bayer Leverkusen, could be key to Emery’s defensive rebuild.
The German experienced a tricky start to life at Arsenal as he waited for a chance to replace Cech, who has struggled to adapt to Emery’s desire for a goalkeeper who can pass out from the back.
Asked if he had been frustrated at being made to wait to make his debut, Leno replied: “Of course, because I came to the club to play every game.
“But I think to move to a bigger club, another country, it needs maybe a little bit of time. It is a little bit frustrating but I keep calm and work very hard to improve.
“I think my performances in training are good. I train very hard and maybe it needs a little bit of time. I keep calm. My chance will come.”
Everton manager Marco Silva could give a debut to Yerry Mina after the former Barcelona defender began training with the rest of the squad last week following a foot injury.
Everton have yet to keep a clean sheet this season and suffered a wretched 3-1 home defeat against West Ham in their previous match.
“It’s something we analysed during the week. They already know what we did in the wrong way and what I expect in the next game that we don’t do the same,” Silva said.
Everton will be boosted by the return of Brazil forward Richarlison after he completed a three-game ban.