Last night the club confirmed Pellegrino had been relieved of his duties as first-team manager, and the 46-year-old leaves them just one point above the relegation zone with eight matches left to be played.
"I think that was probably something that, looking back with hindsight, the club would probably regret, trying to keep him in the summer", said Le Tissier, who scored 209 goals for Southampton during his 16 years at the club.
"The club will look to appoint a new management team as soon as possible, with the search for a replacement already underway", Southampton said.
He has also managed Wales, Manchester City, Blackburn Rovers Fulham and Queens Park Rangers - and is behind only Arsène Wenger, Sir Alex Ferguson, Harry Redknapp, David Moyes and Sam Allardye on the list of most Premier League games. And to think, they sacked Claude Puel for finishing 8th.
Saints chief Reed sees his brand of attacking football, ability to improve players - like Rodgers dramatically has at Celtic since May 2016 - and tactical nous as being perfectly suited for the St Mary's Stadium.
"With a three-week gap before the next Premier League game, they realised this was their last chance to make a change as it did not seem they were going to get themselves out of danger as nothing was changing on the pitch".