Shane Long opened the scoring at St Mary's Stadium before Mane struck three times in a dominant win for the hosts against a City side who made a number of changes ahead of their UEFA Champions League semi-final second leg with Real Madrid.
"The three points was the important thing," Mane told Sky Sports. "I'm happy to score the goals for my team and I hope we keep it going.
"I think all four goals - we're happy with that! We played fantastic football today and we try to work hard for the next games now."
Southampton captain Jose Fonte described his side's showing as "commanding" and admitted it was part of their plan to exploit Mane's pace against a makeshift City defence.
"We were superior and we're very pleased," he said. "We knew they could have started quickly in the second half but we were prepared for it.
"The game plan was to explore the pace up front, the willingness to run and chase the ball and exploit the space. We were very confident on the ball and Mane was on fire today."
Southampton are now two points behind sixth-placed West Ham in the English Premier League table and Fonte is eager to keep fighting for a UEFA Europa League spot, with Ronald Koeman's side heading to title-chasing Tottenham next week.
"It's important to be in the fight - you never know what can happen in the Premier League," he added. "We look forward to the Spurs game now."
