But in an open letter on Southampton's official website, Pellegrino said: "I feel so sorry to leave the club in this situation".
With the form Southampton have been in this year, Pellegrino's sacking has been more of an inevitability than anything else, but with only eight matches left in the season, it puts the club in an incredibly hard position.
Hovering just one spot above the relegation zone Southampton are in danger of losing the top-flight status they acquired six seasons ago.
The club finished eighth in the Premier League previous year and reached the final of the League Cup.
The Argie boss, 46, was axed on Monday after a dire run of form left the Saints just one point above the bottom three.
Hughes began his managerial career with the Wales national team and subsequently managed Blackburn, Manchester City, Fulham and QPR.
The Saints are now occupying 17th position on the Premier League standings with 28 points from 30 games.
Club chiefs will want to make an appointment quickly with an FA Cup quarter-final against Wigan on Sunday.
Hughes will have his work cut out to do that with Saints still to play Arsenal, Chelsea, Everton and Man City in their final eight games of the season, while five of the eight games are away from home.