Le Tissier said he was stunned by news of Adkins' exit and replacement by Mauricio Pochettino - and slammed Cortese for his failure to account for his decision at a subsequent press conference.
Le Tissier told BBC Radio Five Live's Sportsweek: "I don't know if Nigel was becoming too popular and the chairman didn't like it - he does appear to have a bit of an ego problem.
"It is a little bit bizarre, but some of the decisions that have been made have been a little bit bizarre since the current chairman took over. In a way it wasn't a surprise because I think he's been looking to get rid of him for a while now.
"The strangest thing about it all for me was he brings the new manager in about a minute after he sacked Nigel and then he hangs the new manager out to dry at a press conference on his own, which I thought was an incredibly cowardly thing to do.
"If he's going to make those decisions surely he owes it to the fans to sit there and explain his decision, but he wasn't brave enough to do that."