Le Tissier believes that Cortese's failure to explain his decision or turn up for Pochettino's first press conference as manager proves that he is a coward.
He told The Sun: "Maybe Nigel was becoming too popular and the chairman didn't like it. He does appear to have an ego problem.
"He made that decision but then brought the new manager in a minute later and hung him out to dry alone at a press conference.
"I thought it was a dreadfully cowardly thing to do. You owe it to the fans to sit there and explain the decision."
Saints begin life under the former Espanyol coach with a home match against Everton tonight.