The Liverpool forward struck for the third time in the past two matches in first-half stoppage-time at St Mary’s, where the Reds went on to win 2-1.
Collecting Milner’s pass just inside the Saints area, Mane held off the attentions of the opposition defence and powerfully whipped a finish into the top corner.
“I thought it was really open between two defenders,” the No.10 told Liverpoolfc.com.
“So when I saw Millie I knew he was going to give me the ball, then I saw the man, no-one was close to me, they stood off and I tried to go a bit outside and put the ball inside.”
Despite returning to training less than a fortnight ago, Mane has made a hugely impressive start to the 2019-20 campaign.
The Senegal international notched a double in the UEFA Super Cup final against Chelsea, then added an assist for Roberto Firmino to his own effort at Southampton.
“I’ve been working so hard and will keep on working hard,” he said, when asked to rate his current level of form.
“That’s it, I’m just trying to do everything to help my team. And, at the end of the day, the important thing is the three points.”
Liverpool shrugged off a tight turnaround between their exertions over 120 minutes and a penalty shootout in Istanbul on Wednesday and the need to perform again on Saturday.
Mane insisted their success in maintaining a 100 per cent start in the Premier League was as much in the mind as in the physical effort.
“We know it’s part of our job,” he added.
“After playing 120 minutes in midweek it wasn’t too easy but we have to do it and we tried to recover well, come back stronger and try to give everything to try to win the games.
“I think the tiredness is here [points to his head]. It was a really important three points, really important.”