Forgotten striker Emmanuel Adebayor scored twice in the Barclays Premier League clash at St Mary's, cancelling out Adam Lallana's opener before sealing the win in the 64th minute after Jos Hooiveld's own goal matched Rickie Lambert's score.
"I never said I wanted the job and I never said I don't want the job," Sherwood told Sky Sports 1.
"I've got to talk to the chairman and see where they want to take this football club."
Asked when that will be, Sherwood said: "Sooner rather than later as these players need a manager.
"Hopefully I will speak to the chairman tonight. I don't want it (the job) on a temporary basis. I want it for the long term. It's got huge tradition but at the end of the day its got to be right for me."
It was the second game in charge for the former Blackburn and Spurs midfielder, and unlike the Capital One Cup defeat by West Ham in midweek, this match ended with a much more favourable result for the north London club.
"You enjoy when you win. I didn't enjoy the first half," Sherwood said.
"I thought we were poor and didn't keep the ball enough. In the second half after we had a chat we took it on and showed what quality players we have.
"Emmanuel has not been playing so it doesn't take much (to inspire him).
"In the second half they (Adebayor and Roberto Soldado) looked a threat. It's a squad game. They've all got to take their part. There are a lot of games coming thick and fast."
When asked about the formation he had chose, Sherwood added: "It's my way. It's the way I like to set teams out. There are no rules. There are different ways to win football matches. You do what you beleive and that's the way I think you should win football."
Cast aside by Villas-Boas, Togo striker Adebayor has started both matches under Sherwood and added a brace against the Saints to his strike in the midweek loss to the Hammers.
Adebayor said: "I want to thank all my team-mates, they have been there for me, they tell me to keep working hard and my chance will come.
"To be here today I am very pleased, not just the goals but for the team and I am very happy for the new manager, the fans. They have been supporting me."
The 29-year-old also revealed words of encouragement from Sherwood had given him the boost he needed to be successful, in light of some difficult family circumstances.
"He (Sherwood) told me 'Emmanuel, I know you for a long time' and he was with Harry, he told me 'I need you, get out there, play your football, I will not tell you anything, you have been around the block, Arsenal, Manchester City, Real Madrid', you know how to play.
"For me, that was big confidence, the new manager telling me that, and I am very happy for him.
"Not only a few months but 2010, 2012, my brother passed away, it was emotionally difficult, he was my senior brother, for me, it's for him.
"He left a son behind. I want to take care of him and his family. I went to the funeral and when I came back I lost my place in the team.
"I kept doing my job and as my father told me 'keep working hard'. Today it paid off and I am very happy."