Southampton denied Manchester City a win at the Etihad on Saturday by forcing the defending champions to a goalless draw.
Pep Guardiola's men have now dropped their fifth point of the season after opening day 1-0 loss to Tottenham.
City who netted 10 goals in their last two Premier League home matches (five apiece against Norwich City and Arsenal) failed to record one against the Saints.
Ralph Hasenhüttl's men had a penalty in the 61st minute after Armstrong was brought down by Walker but the decision was overturned after a lengthy VAR check, with referee Jon Moss going over to the touchline monitor before overturning his original decision.
Raheem Sterling thought he netted a late winner for City but it was overruled for offside by VAR.
Saints returned home with a valuable point while City dropped two with their first draw of the season.
Meanwhile, Liverpool beat Patrick Viera's stubborn Crystal Palace 3-0 to go top of the EPL summit.
Sadio Mane netted his 100th goal for the Reds to give the hosts a 1-0 lead into the break.
Mohammed Salah and Naby Keïta sealed the win in the second half to send Jurgen Klopp's men top of the table after four wins and one draw.