Seasiders boss Ian Holloway claimed that a Premier League side had tapped up the 21-year-old, with some weekend reports identifying Saints as the team in question.
Holloway said: "Somebody has made an illegal approach and we can prove that."
But Adkins, while admitting Southampton had been in contact with Blackpool about Phillips, insists the club has acted responsibly.
"It's a shame that Blackpool have had to go and do things via the media in the way that they have done," he told the club's official website.
"I don't think there is any hiding from the fact that Matt is a player that we have been an admirer of for the past few years, and in the last couple of weeks he has probably been identified as a target for a number of teams in the Premier League.
"I know that from the chairman's point of view he has been in contact with the Blackpool chairman and that we have had a conversation with their chief executive.
"I have spoken to Ian Holloway myself, so it's not as if there has not been an interest demonstrated from Southampton .
"As I have said, we like to think that we do everything properly, by the book, and we will continue to do our matters privately and behind the scenes.
"Obviously, this situation has now arisen and we will take action on that and respond in the appropriate manner."