The result leaves them just one place and one point above the relegation zone.
Whoever is appointed will be the club's fifth permanent manager in the five years since Mauricio Pochettino, now Spurs manager, replaced Nigel Adkins.
Southampton's next match is an FA Cup quarter-final at Wigan on Sunday, before a crunch clash with relegation rivals West Ham at the London Stadium on March 31.
Hughes quickly overtook Silva at the top of the market last night, with the Welshman cut to just 4/11, although he's now hovering around the 1/2 mark in the betting. Hughes has never been relegated as a Premier League manager and with his former club Stoke also in the PL relegation battle with Saints, it may be a way to show his former employers what they're missing.
"As you know, my period in Southampton has finished".
"I have to say thanks to Ralph (Krueger, club chairman), to the board, to Les (Reed, executive director) and Ross (Wilson, director of recruitment and scouting), all my technical staff and all the Southampton employees".
"From the beginning I tried to do my best every single day", Pellegrino said in a statement published by the club.
"Some moments we managed this, some moments we couldn't, but we have been living a hard season for many reasons".
Southampton's predicament, and the fact that Hughes is the strongest candidate that ticks their boxes, means that the 54-year-old manager holds some leverage over the club he played for more than 50 times in the 1990s.