Pellegrino supervised only five wins in his 30 association games with Southampton following his accomplishment in June.
The 46-year-old arrived at St Mary's as the substitution for Claude Puel, who was took despite leading Southampton to an eighth-place complete and the association crockery closing.
a 3-0 overpower at authorization contestants Newcastle over the weekend left Southampton just one place and one component above the bottom three.
With Southampton advocates labelling for his judgment, the Argentine coach's opening was confirmed on Monday and he evaluated it was fatal given his nonaccomplishment to inaction the slide.
In a message publicized on Southampton's computer on Tuesday, Pellegrino expressed: "From the commencing I strove to do my champion every individual day, I strove to give back to the club and strove to equal the club with feeling.
"Some times we supervised this, some times we couldn't, but we have been living a strenuous season for many reasons.
"The administrator is the face of a lot of preferences and acts, but I always attempted to put the club first with my technical force and the committee behind me.
"I feel so sorry to leave the club in this situation, but when you don't get results I understand the decision the club has to take."
Southampton have triumphed just one of their last 17 association matches and have only eight games to rescue their top-flight states.
deities will be wishing to select Pellegrino's peer quickly, with a fa crockery quarter-final at Wigan looking on Sunday.
They then face a noise noise with authorization contestants region Ham at the London playground on March 31.
Former husk master Marco Silva is the early rival to regenerate Pellegrino after being took by Watford earlier this season.