"For sure Charlie has a hamstring injury, (that's) what I heard from the doctor," Koeman told the club's website (www.saintsfc.co.uk).
"Shane got a kick on his knee and I think that's not so bad, but I think Charlie will be out for several weeks."
Koeman also urged his players to show more hunger after Southampton suffered their first league loss to their south-coast rivals since 1958.
"There was a big difference in how they (Bournemouth) started the game, how they were hungry and were winning challenges," Koeman told reporters.
"If you analyse the game and ask every (Southampton) player if they won or lost most battles all ten will recognise they lost more battles. Normally I defend players but not today. They (Bournemouth) were more hungry than we were on the pitch."
Having lost back-to-back league games for the first time in two months, Koeman's seventh-placed Saints have a chance to get back on track at home to fourth-bottom Sunderland on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Ken Ferris)
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