The left-back, who is on loan at St Mary's from Chelsea, has been part of a side who have grabbed six victories from nine matches.
Many tipped the Saints for relegation this season following a mass exodus of their players in the summer, as well as the departure of manager Mauricio Pochettino, but Koeman's side currently sit second in the table, four points behind leaders Chelsea.
"Probably from the outside [you couldn't have predicted this] when you see a club lose a lot of players and a manager — a manager more so, for me," the Irish Examiner quotes Bertrand as saying.
"But the people behind the scenes at Southampton have brought in a world-class manager and world-class players. As soon as I came in and saw the players, saw everyone training and what they're capable of, it's not a surprise to me."
Next up, Southampton will face Stoke City in the Capital One Cup on Wednesday.