The Saints top Group A with United in second place ahead of the 1pm kick-off at Whitley Park, and a draw could be enough to send both teams through to the knockout stages.
But Beardsley would prefer his side to be the masters of their own destiny at the end of a group campaign which has seen the Magpies beat Bristol City home and away, draw and lose to Swansea and slip to a 3-0 defeat against Tuesday's opponents in early December.
"The winner takes all," Beardsley told nufc.co.uk.
"Southampton will think the same; if they win, they're guaranteed to top the group so it is what it is, and it's great. We were disappointed to lose to Swansea away but the boys have done well and the two Bristol City games were good.
"Southampton deserved to win down there so it'll be a tough game, we've got no qualms about that. Because of the EFL Cup final on Sunday, they may send a young team but when you look at the players they have produced it's amazing, and fair play to them."
Beardsley hopes to welcome forward Tom Heardman back from injury and is determined to progress to the last 16.
Bristol City and Swansea meet at the beginning of next month and a draw there would still be enough to send Newcastle through regardless of Tuesday's result.
He added: "We think the format is good - it's six more games for the kids and the more games, the better.
"If we can get the result against Southampton, that prolongs it. We have a really good chance of making the play-offs in the league, too, so the kids have been brilliant. They've had a great year.
"Simon (Tweddle, fitness coach) and Ben (Dawson, professional development phase coach) have got them in a great place in terms of fitness and understanding and Carl (Nelson, physio) and Chris (Terpcou, goalkeeping coach) have done their bit.
"It's all been good and we're looking forward to an exciting end to the season, whereas in recent years there hasn't been as much to play for."
Admission at Whitley Park is free to season ticket holders and members, or £3 for adults and £1 concessions.
