The 24-year-old midfielder led the side for the first time in Sunday’s 3-2 defeat at Manchester City, nearly helping the club record a famous opening-day result against the defending champions.
Academy graduate Lallana, who has been with Saints since the age of 12, cut a proud figure at the Etihad Stadium, particularly as he strode out from the tunnel at the head of the line before kick-off.
And Davis insists there is no one else at the club he would rather see in possession of the armband.
“It’s fantastic for Adz,” he said. “He’s spent a long time at the football club and he’s come through the ranks.
“I’m pleased, he’s a good lad and a good friend, and I wouldn’t wish anyone else in the team to have it.”
Davis used to wear the armband himself, before he agreed with ex-manager Alan Pardew that an outfield presence would be more suitable.
Now, though, the baton has been passed again.
Davis, who has always retained the role as club captain, believes that Lallana has all the attributes to make both a magnificent leader and player in the Premier League.
“I hope that he can really go on and grow as a player in this league and, certainly, if he’s got the armband on while he does it then fantastic,” said the keeper.
“I think when you get that armband on it does give you something extra and it certainly gave something extra to Adam (at Manchester City).”
Lallana clocked up his 194th first-team appearance for Saints at the weekend, with Adkins revealing that he felt the time was right to bestow the honour on him.
“It again just epitomises the vision we’ve got,” said the manager.
“He’s been with us since the age of 12. He trains so hard every day and I think he’s now ready to go and be a leader, and at a young age I’m going to give him the opportunity to go and do that.”