"In my opinion he was the best player on the pitch, and that's all the credit," Koeman was quoted as saying by the British media.
"No pre-season for three months out and playing like he wasn't away of the team and that was very good."
Bertrand played a key role last season making 34 league appearances, as he helped Southampton to a seventh-place finish in the table, their highest ever finish in the Premier League.
Deadline day signing Virgil van Dijk scored his first Saints goal against the Swans and Koeman said he was confident the defender will play a key role for the club this season.
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"He's only 24 years, it's his first season in the Premier League and he will improve, he will learn and he can be better," Koeman said.
"Of course that's one of his qualities. A good header, he's defensively strong, he has good free kicks, a good shot out the box. His personality is important for the team," he added.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
