Seasiders boss Ian Holloway has said that he will report an unnamed club, believed to be Saints, to the Football League over their attempts to sign Phillips.
Adkins is unhappy with Holloway, telling the club's official website: "It's a shame that Blackpool have had to go and do things via the media in the way that they have done.
"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.
"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, and I have spoken to Ian Holloway myself. Obviously this situation has now arisen and we will take action on that and respond in the appropriate manner."
Adkins made the comments in a post-match press conference after Southampton were thumped 4-0 by Champions League qualifiers Udinese in a friendly at St Mary's on Saturday.