Unai Emery says Arsenal cannot qualify for next season's Champions League if they continue to drop points against the Premier League's lesser clubs.
Gunners manager Emery saw his side's 22-match unbeaten run in all competitions halted by a 3-2 defeat at struggling Southampton.
Sunday's setback leaves the London club three points behind fourth-placed Chelsea in the race for European football.
"We need to be very, very demanding of ourselves, like we are.
"After 22 matches unbeaten we didn't lose and we are only fifth position in the table and the reason is because other teams are very well."
Henrikh Mkhitaryan twice levelled for Arsenal at St Mary's to cancel out headers from Danny Ings, before substitute Charlie Austin grabbed Saints' late winner.
With Sokratis Papastathopoulos and Shkodran Mustafi suspended and Rob Holding injured, Emery was forced to field a makeshift defence.
Captain Laurent Koscielny, a long-term absentee with an Achilles problem, made his first top-flight appearance since April, while midfielder Granit Xhaka was selected as a left-sided centre-back.
Despite conceding three times from crosses into the box, Emery said he was satisfied with the performances of his defenders and was pleased to see Koscielny come through unscathed.
"I think they worked very well," he said of his backline.
"For example, today very good news for Koscielny, very good performance in 90 minutes.
"And other players, like Xhaka, played well.
"Chances for them (Southampton) not a lot, but their efficiency today is good."
The Gunners also lost Hector Bellerin to a calf injury on the south coast.
Speaking about the right-back's problem, Emery added: "He has a small injury but I think he's going to be some weeks off."
Austin's 85th-minute header gave Southampton boss Ralph Hasenhuttl a dream home debut to move the team out of the relegation zone.
Austrian Hasenhuttl sent beer tokens to Saints' season-ticket holders before the game and his gesture had the desired effect at a raucous St Mary's.
The 51-year-old, who replaced the sacked Mark Hughes on December 5, charged on to the pitch at full-time to celebrate the club's first home win since April.
"First I have to apologise to Emery that I didn't shake hands immediately because I didn't see him," said Hasenhuttl.
"I had to run to my guys because they were waiting. I did it (shook hands) later and it was OK.
"It's what I wanted to feel when I came to the Premier League, this atmosphere after the game and to celebrate such a moment is something very special for me.
"To come back again and again and again it was amazing because it showed us we have the character to face problems and to make the next step."
Asked about the free drinks, he added: "I think it was the perfect step to help us.
"I heard when it works like this you have to do it every game at home. We'll have a look."