Ancelotti only arrived back in England on Saturday morning in order to take charge of Chelsea's game against Rovers and labelled their five-goal super show as the "best performance" since he took charge at Stamford Bridge.
"It has been difficult time but this is life," said Ancelotti. "I hope my father will be better in the next day."
He added: "I have a free day and will go back to Italy and return on Monday but I think my father will be better.
"These are difficult days but after Monday I think he will be better and I can stay here without problems."
Frank Lampard scored twice, once from the penalty spot, and other strikes from Didier Drogba and Michael Essien plus an own goal from Gael Givet put Chelsea back on top of the Barclays Premier League.
Ancelotti was certainly cheered by a superb individual performance from returning Joe Cole.
The England midfielder, out for 10 months after damaging his knee ligaments against Southend in the FA Cup last January, produced a performance full of trickery and flair against Rovers.
"I was impressed with Joe because I know very well how hard he has worked in the last month," added Ancelotti. "He is a great professional and after 10 months it is not easy for Joe to play like he did. It was a surprise and I am happy for him.
"Joe is a very important player for us. He has fantastic quality in midfield. He is a genius."