The Saints, bidding to follow in Norwich's footsteps and win back-to-back promotions, currently occupy the second automatic promotion spot in the npower Championship and Adkins will rest some key players for the fourth-round replay at St Mary's Stadium.
Teenagers Luke Shaw, James Ward-Prowse and Jack Stephens are set to be involved again.
Adkins said: "Having put ourselves in the race to get promoted, the league is the priority.
"But it's great to have a cup run and we want to win all the games we compete for and we want competition for places.
"We've got a good, strong squad of players and now and again we want to utilise the youth. We've done that in the two cup competitions this season."
Millwall turn their attention to the cup after Saturday's defeat at derby rivals West Ham left them hovering just above the relegation zone.
The Lions are set to be without captain Paul Robinson (thigh) and deadline-day signing from Wolves, Andy Keogh, is ineligible, so Tottenham loanee Harry Kane or former Saint Dany N'Guessan will start up front.
Hamer Bouazza, Jordan Stewart (both groin), Tamika Mkandawire (knee) and Therry Racon (ankle) are still out.
Blackpool manager Ian Holloway says his class of 2012 can stand shoulder to shoulder with any of the club's famous names from the past as he prepares his side for tonight's replay at Sheffield Wednesday.
Holloway, whose side snatched a replay thanks to Kevin Phillips' last-minute penalty at Bloomfield Road nine days ago, said: "I'm very proud of the will to win that we're getting again after all the disappointment of losing arguably some of the best players this club has ever had.
"Charlie (Adam), Vaughany (David Vaughan) and DJ (Campbell) - I would put them in the same list as some of the famous ones we've had before because getting to the Premier League and almost staying up with 20 minutes to go at Manchester United, they've got to be up there with some of the greats."
Wednesday boss Gary Megson said his side's cup run was not a hindrance, for now, as he attempts to guide them back to the Championship this season.
Aldershot, Morecambe and West Ham have come unstuck against Wednesday in previous rounds and Megson said: "There's two ways of looking at it. You're playing all the time and everybody's got that interest, and it's good financially. At the moment we're doing ok in terms of injuries."
Owls centre-half Rob Jones (ankle) will return from a four-game lay-off in place of cup-tied Miguel Llera.