Koeman's side booked their place in the FA Cup fourth round on Wednesday with a 1-0 win at Portman Road, but were forced to replace Wanyama at half-time.
The Kenyan midfielder appeared to hurt his hamstring and joins an injury list that also includes Morgan Schneiderlin and Toby Alderweireld.
Koeman expects Wanyama to miss a number of games, with a clearer diagnosis set to be confirmed on Thursday after a scan.
"Victor Wanyama is a pity. Before the match I spoke to him and told him he would have 45 minutes, and he got injured with 10 seconds of the half left," explained the Dutchman.
"He will have a scan [on Thursday] and we will see, but he will be missing for a few weeks."
The Premier League side were rarely troubled by their Championship opponents in the third-round replay, with Shane Long's first-half strike proving the winner.
Koeman explained his delight at Southampton's showing against a side flying high in the second tier amid blustery conditions in Suffolk.
"We played with very good organisation. It was difficult, it was tough and it was difficult to play out there," he added.
"There were a lot of long balls and battles and we scored with our first chance.
"We kept another clean sheet and that is important. We were prepared for the game and we showed that."
Mick McCarthy, Koeman's opposite number, was left frustrated by Long's goal, which fell for the Irishman following a challenge from Luke Chambers on Harrison Reed.
However, McCarthy backed his side to bounce back in their quest for promotion from the Championship.
"We gave away a soft goal and then didn't create many chances. Southampton are a good team and have the best defensive record in the Premier League," he told the BBC's Match of the Day.
"Whenever you lose it's always a dampener but it's not going to throw us off course."
