The Gunners had to twice come from behind in front of their home fans as goals from Alexandre Lacazette rescued a point for the struggling Gunners against the Saints at The Emirates on Saturday.
Emery has found himself under increasing pressure in recent weeks, with his side having only won four of their opening 13 games in the Premier League this season.
Their miserable form has left Arsenal well off the pace in the race for a top-four finish and Champions League qualification this season.
Boos rang out around The Emirates after the final whistle on Saturday afternoon as Arsenal fans made their discontent with the situation heard.
Emery insisted after the game that he fully understands the frustration of the home fans.
Speaking at his post-match news conference, Emery said: “I understand the supporters are angry.
“The players are feeling the same and my job is to find out how to improve and the key is here with the supporters.
“Our target was to win but above all the play well and we didn’t do that.”
Asked if he still has the support of the Arsenal hierarchy, Emery added: “They are supporting me every day.
“I know we can do better and I’m going to try to do that.”
Arsenal will return to Premier League action next weekend with a trip to Norwich City in the top flight.
Before that, they will take on Eintracht Frankfurt in the Europa League on Thursday night.
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