The Saints are at Stevenage in the second round of the competition on Tuesday.
"Obviously it gives us an opportunity for some of the players who haven't started the last two games to start so there will be a bit of rotation," said Adkins.
"We will be taking it seriously, though. We want to win every game of football. If you have got a shirt on playing for Southampton, you have a winning mentality that we have here.
"We want to go out and endeavour to win every game of football."
Southampton have lost both their Premier League games this season.