The Gunners slipped to their second successive Premier League defeat despite Joel Campbell making the breakthrough in the first half at the Emirates Stadium.
Former Crystal Palace winger Wayne Routledge levelled for the Swans before half-time as Swansea looked to avoid successive defeats in north London following Sunday’s 2-1 loss to Tottenham Hotspur.
Swansea captain Ashley Williams scored a second-half winner to condemn Arsenal to their third consecutive defeat in all competitions.
Speaking to BBC Sport following a dramatic game at The Emirates, former Manchester City defender Mills revealed Arsenal’s downfall against the Welsh side.
“Swansea only had two shots – well, Arsenal only had five shots!” Mills said.
“Arsene Wenger will always say they were unlucky but you have to put the ball in the back of the net.”
Arsenal are in third place but six points behind leaders Leicester City after the Foxes played out a 2-2 draw with West Bromwich Albion at King Power Stadium on Tuesday night.
Arsene Wenger’s side face title rivals Tottenham at White Hart Lane in Saturday’s early kick-off.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news