Salvaging a top-four finish in the Premier League would at least ensure the London club start next term in no worse a position than this season albeit with exactly the same problems to solve as they had when they installed Villas-Boas last June.
Failure to grab a qualifying spot for Europe's elite club competition would mark their worst season since Roman Abramovich bought Chelsea in 2003 and could shrink the pool of managerial candidates even more than the reputation of the job might.
Former assistant Di Matteo has 11 league games in which to lift Chelsea from the fifth place they currently occupy or the club will not even be in the competition their Russian owner values more highly than any other.
The Italian former Chelsea midfielder, who has managed in the English top flight before with West Bromwich Albion, has the backing of former assistant coach Ray Wilkins.
"He knows the situation in the Premier League, he's been around for quite a while," Wilkins told Sky Sports News.
"I'd say it was probably better that Robbie takes over than bringing someone in for the rest of the year."
Villas-Boas was dismissed on Sunday after a poor run of results, leaving the club three points behind fourth-placed Arsenal and on the brink of a Champions League exit.
UPHILL BATTLE
Di Matteo's first match in charge will be Tuesday's FA Cup Fifth Round replay at Championship Birmingham City in the only competition they still have a realistic chance of winning.
They host Stoke City in the Premier League on Saturday before facing an uphill battle to try to overturn a 3-1 deficit at home to Napoli in the second leg of their Champions League last-16 tie.
There has been no word on whether Di Matteo is seen as a potential candidate for the longer term but with Abramovich having already been burnt by his gamble on an upcoming manager in Villas-Boas, he seems likely to go for a bigger name.
There has been much media speculation over a possible move to lure fans favourite Jose Mourinho back to the club he led to successive Premier League titles in 2005 and 2006 but a lack of Champions League action could put off suitors of his calibre.
Whoever takes the job on a permanent basis, or at least as permanent as any Chelsea post is with Villas-Boas shown the door less than nine months into a three-year deal, will be under no illusions about what is expected of them.
Even Mourinho could not bring Abramovich the European Cup, while Avram Grant was fired after taking Chelsea to the Champions League final and Carlo Ancelotti was given his marching orders after a trophyless season despite winning a league and cup double the previous year.
"You need to bring results and good football, this is the target of Chelsea," Grant told Sky Sports News. "The owner has made this clear and he has put a lot of money in to do things in the right way. This is the name of the game."
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