Shaw became the most expensive teenager of all time when he moved from the Saints to Manchester United for a reported £33 million earlier this summer, while captain Lallana joined Liverpool for around £25 million.
The South Coast club's squad has been decimated with departures and Chambers became the latest high-profile exit when he made the switch to Arsenal for around £16 million on Monday.
Lallana and Shaw's rise has been meteoric, and the pair were included in the England squad for the Three Lions' ill-fated World Cup campaign.
Adkins, who was sacked as Saints boss in January 2013, managed all three at St Mary's, and gave Shaw his debut as a 16-year-old, and he explained how they will prosper in their respective new surroundings this coming season.
Speaking about Lallana, Reading boss Adkins told Sky Sports News: "Adam Lallana was the best trainer, every day. And his enthusiasm and his desire to keep improving [was there for all to see].
"He loved football and his passion rubbed off on everyone else. He's got a great attitude and work-rate that you just love and a desire to keep improving."
Adkins had similar words of praise for 19-year-old defender Chambers, and said that the teenager's attitude will take him to the top of the game.
"To see Calum having his move to Arsenal, having played 20-odd games in the Premier League last season is great," he added.
"His attitude is fantastic is great, his willingness to keep working hard, that's what it's all about to improve on all aspects of your game. His feet are well and truly on the ground, he's got a great manner about himself, and I think that speaks volumes."
Finally, Adkins claimed that he feels Shaw will take time to adjust to playing for a club the size of Manchester United.
"When we had Luke, he played in the youth team and he couldn't last a full game, and gradually, he got to the stage where he could last a full 90 minutes of the intensity of the Premier League, it's the highest level," said Adkins.
"He's just been to the World Cup with England, he's probably had two weeks off to recover and he's just had an unbelievable move to Manchester United.
"So all these things are going on, not just physically, but mentally, and like any new player, you've got to adjust and I'm sure the manager will do everything to manage him and develop him."
Southampton have also lost Rickie Lambert and Dejan Lovren to Liverpool, and Morgan Schneiderlin could become the latest star to leave after the France international midfielder reportedly handed in a transfer request in an attempt to force a move to Tottenham Hotspur.
Southampton also lost their manager Mauricio Pochettino in the close season, and his replacement Ronald Koeman has his work cut out for him as he looks to significantly strengthen the side ahead of the new campaign.