Puel, who was sacked after just one season in charge in which he took Southampton to the League Cup Final and a top-half finish, left his replacement Mauricio Pellegrino with a chorus of boos at the full-time whistle.
Southampton has just one win in their last five games and sits just five points above the relegation zone, and faces a daunting festive season with fixtures against Chelsea, Tottenham and Manchester United.
Riyad Mahrez made it a dream start for his new manager when Leicester’s first shot on target hit the back of the net after being unchallenged on his way to the edge of the box on 11 minutes.
Shinji Okazaki nearly doubled the lead nine minutes later only to see his effort, which was deflected on its way towards goal, palmed away by Forster.
Southampton continued to be pressed back as Leicester dominated the opening half hour and Okazaki saw his attempt cleared off the line before Jamie Vardy was kept out from point-blank range.
Okazaki showed Leicester’s intent to win for their manager made it 2-0 as he was first to the rebound after Forster made the initial save on a shot from distance.
Puel wouldn’t have to wait long to rise from his seat with arms waving in celebration as Andy King added a third before the half, tapping in at the back post.
Maya Yoshida managed to pull one back just after the hour mark when he met Ryan Bertrand’s corner, and the comeback was nearly on if it hadn’t been for Kasper Schmeichel denying Charlie Austin from close range.
But Okazaki made it a comprehensive victory with his second of the night as Vardy squared the ball across goal after a counter attack shredded the Saints defence.
Southampton: Forster, Cedric, Yoshida, van Dijk, Bertrand, Davis, Romeu (Gabbiadini 46), Lemina, Tadic (Ward-Prowse 83), Boufal (Redmond 62), Austin.
Unused subs: McCarthy (GK), Stephens, Ward-Prowse, Hojbjerg, Long.
Goals: Yoshida (61).
Bookings: Austin (52).
Leicester: Schmeichel, Simpson, Morgan, Maguire, Fuchs, Chilwell (Ulloa 83), Ndidi, King, Mahrez (Gray 72), Okazaki, Vardy (Albrighton 72).
Unused subs: Hamer (GK), Dragovic, Amartey, Iborra, Gray, Albrighton, Ulloa.
Goals: Mahrez (11), King (38), Okazaki (20, 70)