Bertrand fired his first Southampton goal in Saturday's 2-1 home victory over QPR, after Clyne struck the winner in Tuesday's 2-1 Capital One Cup triumph at Arsenal.
England full-back Bertrand has a Champions League winners' medal and is still a Chelsea player, but is now on his ninth loan stint from the Blues.
Saints boss Koeman hailed Bertrand's quick adjustment to life on the south coast, tipping the two-cap 25-year-old to forge a dangerous attacking partnership with fellow full-back Clyne.
"I'm very happy about him, because if you play for Chelsea then you have real qualities," said Koeman.
"He has adapted to our way of playing extremely quickly and to the ambition of the club.
"Clyne scored on Tuesday, Ryan has scored too and that's important for the team.
"We can't just rely on the attackers for goals, we need more from across the pitch.
"We have different players who have scored this season and that makes the team strong."
Summer recruit Sadio Mane made a lively Premier League debut in Saturday's QPR victory, with Graziano Pelle's acrobatic volley sealing victory.
Charlie Austin fired an impressive leveller for Harry Redknapp's men, only for Italian forward Pelle to trump his strike with a smartly-taken scissor-kick finish.
Former Red Bull Salzburg forward Mane had his Saints career stalled slightly by work permit red tape, but manager Koeman has now tipped him to make up for lost time.
"Sadio had to wait because of work permit rules but now he's in the team and working hard to bring the competition in the team," said Koeman.
"He showed his qualities on Tuesday but now against QPR as well.
"He's very fast
He's always dangerous, because he's so fast and he has good movement in attack
"We need that type of player."
Source : PA
Source: PA