The 42-year-old former France international spent six years at Chelsea, the last of which was the first in the Roman Abramovich era.
Desailly told the London Evening Standard:"I was surprised Carlo Ancelotti was sacked but you don't know what is going on. He was having conversations with people at the club and giving too many excuses for what happened last season for a club that really want to win with a very passionate chairman.
"He is not obsessed with the Champions League. He is calm. The people around him are nervous - the marketing side of the club is not as big as it should be for a club like Chelsea. But Roman is cool. He is happy to make decisions and take gambles. There was life after Jose Mourinho, there will be life after Ancelotti."