Unai Emery fears that slip ups, like the one his team faced at St Mary's on Sunday, could be the undoing of the club's hope to return to the Champions League.
Southampton rose to the occasion under new boss Ralph Hasenhuttl, to bring the 'Gunners' incredible 22 match unbeaten run to an end.
The set back leaves Arsenal trailing London rivals Chelsea by three points, heading into the busy festive fixture list.
After the defeat, Arsenal boss Emery was in bullish mood about both his side's performance, as well as their aspirations for elite level European football come the end of the current season.
He told the media: "Our demand is very big but also the level is very high level with the other teams. And if we don't win like today, we cannot be in the top four."
The Spaniard added: "Other teams usually they are winning but we need to do our way and continue to build. The objective is therefore top but we know it's not easy because the other teams are at a high level. We need to be very, very demanding of ourselves, like we are."
During the defeat, particular question marks were raised over the 'Gunners' defending, especially in terms of dealing with crosses into the box.
Yet in spite of conceding three headed goals, Emery maintained that he was happy with his back line's performance on the south coast.
He concluded: "I think they worked very well. 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."