Senegal forward Mane was impressive throughout in his Premier League debut at St Mary's Stadium on Saturday and set up full-back Bertrand – on loan from Chelsea - for his first Southampton goal and maiden Premier League strike nine minutes into the second half with a clever backheel.
Charlie Austin cancelled out that effort, but a spectacular overhead kick from Graziano Pelle sealed a sixth successive victory in all competitions for Koeman's men.
And the Dutchman was quick to hail both Mane and Bertrand for their impact.
"Sadio had to wait for his work permit, now he is in the team and is working hard to bring the level and bring the competition in the team," Koeman said.
"He's very fast. He was a little bit unlucky in the first 45 minutes but he's always dangerous because he's so fast and he has good movements in attack. We need that type of player."
On Bertrand, Koeman added: "I'm very happy about him because you know if you are a player of Chelsea you have qualities.
"He got the possibility to play for us. I'm very happy because in a fast way he adapted to the way of playing, to the ambition of the club."
