Both players are reported to have been attracting interest from other clubs, but the Saints manager has indicated they will not be leaving.
Adkins does expect a number of squad players to depart this month, but he says the team’s key components will be staying.
Highly-rated teenage left-back Shaw has been the subject of the most speculation in recent weeks, with Arsenal and tomorrow’s opponents Chelsea just two of the Premier League’s top clubs who are keen on signing him.
Reports had suggested that Arsenal officials had planned to use Tuesday’s trip to St Mary’s to open negotiations over the 17-year-old, but Adkins denied this had happened.
When asked if Gunners counterpart Arsene Wenger had mentioned anything about Shaw after the game, the Saints boss said: “No, he didn’t say anything.
“As I have said before, Luke is better playing for Southampton Football Club, where he is being nurtured and looked after.
“He is still only 17 and playing in the Premier League, where he is getting an opportunity to flourish, to make some mistakes and to keep kicking on.
“We have a good culture here. He is under contract, we are not looking to let him go.
“This is best place for him at this point in his career. He has a big, big future in the game, which he demonstrated with his performance against Arsenal the other night.”
Shaw will likely have a further test of his credentials tomorrow when FA Cup holders Chelsea visit St Mary’s for a third round tie.
“I want to go and win the game against Chelsea, but I also have to be mindful that we have had a run of fixtures that are very close together,” said Adkins.
“I have to make sure we arrive on the pitch on Saturday full of energy and not risking anyone picking up a serious injury.”