However, Walker latched on to Angelino's cross to slide the ball home and secure a win that means the champions remain six points behind Liverpool.
"It was a insane game to play, scoring was one of those insane moments".
Pep Guardiola will be keen for his men to keep the pressure on league leaders Liverpool by taking all three points this afternoon and the Citizens will start as overwhelming favourites to do just that.
City and Liverpool were both involved in similar games, needing to fight back after conceding early.
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Ralph Hasenhuttl's side, only eight days removed from their 9-0 humbling at home to Leicester and four days on from a 3-1 Carabao Cup loss here on Tuesday night, defended their unexpected lead superbly for 70 minutes, showing bravery and commitment to deny City clear chances.
It was the visitors who led at half-time having scored against the run of play after a rare mistake by City goalkeeper Ederson, who spilled Stuart Armstrong's low shot and allowed the quick-thinking Ward-Prowse to lift the ball over the Brazilian from close range. Walker grabbed the victor with four minutes to play after Alex McCarthy palmed an Angelino cross in his direction.
"We had most of the ball possession and we caused their keeper lots of problems".
"We were concentrating on our game", said the City right-back, whose appearances in recent weeks have been restricted by illness. It was just a case of hit it and hopefully get the ball in the back of the net.
"If it's one time, two times, "we were lucky, we were lucky", but it happened in the last two seasons many, many times".
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City travel to Italy to face Atalanta in the Champions League in midweek before travelling to Anfield on November 10.
"We know we have a very important week before the break so we have to stay positive and work hard for the next game, and then after doing our job in the week we will focus on Liverpool". The City of a year ago would've dispatched this Southampton team easily, and were lucky to come away with the three points. We have the quality - it is about the mental state of the players.
"Hopefully the supporters were proud of our team and the players".
"It's a great feeling that I can contribute but more importantly it was about the three points".
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Three-time major victor Wawrinka said his three-set final loss to Murray in Antwerp on Sunday proved useful in Basel . The Greek third seed will next face Serb Filip Krajinovic who upset fifth seed Fabio Fognini 6-2, 6-4.