The 60-year-old Italian cut a frustrated figure on the sid-lines at Stamford Bridge as goals from Ander Herrera and Paul Pogba ended the Blues' hopes of retaining their cup crown.
888Sport now make Sarri just 1/5 (1.20) to be the next Premier League manager to leave their position.
The Chelsea boss admitted after the game that his players were still not fully able to grasp the "Sarri-ball" concept which he is trying to instil and some sections of the support appear to be losing patience very quickly indeed.
N'Golo Kante's role in the team has come under increased scrutiny in recent weeks with questions being raised about why the World Cup-winning midfielder has been moved out of his usual position to accommodate the likes of Jorginho and Mateo Kovacic.
In January Sarri explained his players were proving tough to motivate and while the manager doesn’t appear to have lost the dressing room, the recent results have been alarming to say the least.
The frustration with this approach was clear from the home supporters who voiced their displeasure on several occasions during the second half, seemingly questioning Sarri's tactics and substitutions as they tried to orchestrate a comeback against United.
One potential bright spot could be a sustained challenge for the Europa League which would offer an alternative route back to Europe's top table, and Thursday's visit of Malmo should get the Blues back on track after a 2-1 win in the first leg.
A Carabao Cup final clash with Manchester City on Sunday gives Sarri a chance to win some silverware in his first season in England. Pep Guardiola's men are made overwhelming favourites at Wembley though, priced at just 1/3 (1.33) to lift the trophy and 8/15 (1.53) to win in normal time.
That's hardly a surprise given that City mauled Chelsea 6-0 at the Etihad Stadium just over a week ago and with the underdogs enduring a dismal run of form.
In the Premier League Sarri's side have lost three of their last four matches and having slipped below Arsenal into sixth spot, it appears time may be running out for the man who has been in charge at Stamford Bridge for just seven months. Should he remain in charge, Chelsea's next top-flight clash comes against Tottenham on February 27.
While they remain the team to beat in the Europa League at 9/2 (5.50) together with Napoli, questions continue to be asked about whether Sarri will remain in charge long enough to take charge of any potential last 32 clash - should Chelsea make it past Malmo on Thursday night.
Elsewhere in the market Everton boss Marco Silva is 5/1 (6.0) ahead of Claude Puel (11/1) and Claudio Ranieri (18/1), all of whom seem unlikely to be in immediate danger despite some poor results of late.