The duo were both introduced at half time by Saints boss Koeman, replacing Jordy Clasie and Dušan Tadić with the hosts trailing 2-0 to Jürgen Klopp’s side.
Despite missing a penalty shortly after his introduction, Mané netted Saints’ first and third, while Wanyama proved crucial in controlling the midfield during the second 45.
Discussing the impact of the duo, Koeman told youtube.com/southamptonfc
: “I think it was first of all Victor in the midfield. We needed to have a really strong player in that position, because we lost a little bit of the control in the midfield.
“We made the decision after half time. I think really we needed more physicality in the midfield. He was winning second balls and that gave everybody more confidence.
“Sadio is a different player, he is faster than Dušan and that’s what we tried to do, to play with him from the right, Shane [Long] from the left, with the midfielders supporting [Graziano] Pellè.
“That worked fantastic.”
And Koeman was delighted with the belief Mané showed, especially after missing the penalty.
“It’s been a difficult time for Sadio, because the player always likes to start and he didn’t start. It’s not always about one player,” Koeman added.
“He showed great belief in himself and that’s the Sadio we like to see – scoring. He’s a fantastic player.”