However, Emery played down the possibilities of solving the team's defensive issues in the January transfer window, saying it will be hard to find the right player. "We are giving young players chances but we need a high level in the squad".
Defender Sead Kolasinac was a late withdrawal at St Mary's due to tightness in a thigh muscle, while right-back Hector Bellerin limped off with a calf problem and, according to Emery, could miss "some weeks".
That's bad news for Arsenal, who are facing five games between Wednesday and January 1, starting with a Carabao Cup quarterfinal against Tottenham. But also we are in a (good) way. "It's not easy. January is not good for transfers, but we are going to look". Granit Xhaka, Matteo Guendouzi and Lucas Torreira play, while Henrikh Mkhitaryan and Alex Iwobi support Pierre-Emerick Aubameyang.More news: Wantage MP urges Tories to support Prime Minister Theresa May
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All three of Saints' goals came from headers following the visitors' failure to deal with balls into the box.
Unai Emery conceded that Arsenal can not afford to lose against teams like Southampton if they are to finish in the top four of the Premier League this season.
"We need to be very demanding of ourselves, as we are". We also had chances to score more than the two goals but we didn't score.
The shock victory was Saints' first in 15 matches in all competitions, but the Austrian insists his team can not rest on their laurels.