Unai Emery's position at Arsenal is under increasing scrutiny after the Gunners' poor start to the Premier League season.
The 2-2 draw with struggling Southampton left the north London side eight points behind fourth place Chelsea in the race for Champions League football.
Emery admitted after the game that he was fully aware of the supporters' anger, and said he understood why the fans booed his team off the pitch at the final whistle.
we are disappointed, we are frustrated and I understand the supporters.
"We did deserve more today," he said on Saturday.
"We lost a very good opportunity to connect with our supporters, they helped us but really we know here (Emirates Stadium) is the key. To feel comfortable and strong here to take confidence but we didn't do that.
"The first-half, we were drawing but how we were playing wasn't enough. We started the second-half better, we changed and I think it was the best 20 minutes of the whole season.
"We created chances, we didn't score but I was happy in that moment because I wanted to look at our players. Then, they scored we were better maybe and we took some risks after that to draw but we conceded more chances.
"We drew in the last minute but that's not enough. Really, we and the fans can be disappointed and angry because of the result."
Emery had received a vote of confidence from the Arsenal board before the international break, but the rising discontent among supporters and poor performances on the pitch have forced Gunners chiefs into a rethink about potentially parting company with the Spaniard.
In terms of who could replace Emery, reports have claimed that the Arsenal hierarchy have sounded out former Juventus manager Massimiliano Allegri along with Manchester City assistant Mikel Arteta.
There has also been a suggestion that the Gunners could turn to assistant first-team coach Freddie Ljungberg.
The 42-year-old has not yet had a senior managerial role, having coached Arsenal’s Under-15s and Under-23s to date, as well as working at Wolfsburg and Arsenal as first-team assistant.
The Swede is valued highly at the club, though, and would be a prime candidate to at least take over as caretaker, according to The Independent.
However, Ljungberg would not be able to work as a temporary head coach for longer than 12 weeks, according to UEFA rules.
The former Arsenal winger only holds a UEFA 'A' licence, which would allow him to take charge at the Emirates for three months maximum.
He would be required to gain his UEFA Pro Licence, if he has aspirations of filling the Arsenal hotseat permanently.
The Pro Licence is the highest coaching certification available and generally follows the completion of the UEFA 'B' and 'A' licences.
The qualification is also required for anyone who wishes to manage a football club in the top tier of any European nation's league system on a permanent basis - longer than 12 weeks.
Such a licence is also required to manage in the Champions League - or the Europa League, where Arsenal face Eintracht Frankfurt on Thursday.
