Ancelotti's men finally won their 10th Champions League at the end of 2013-14, ending an agonising 12-year wait for La Decima by beating Atletico Madrid 4-1 after extra-time in Lisbon.
Benzema says the Italian's style has been very different to that of Mourinho, and also spoke about the Portuguese boss famously describing playing with the Frenchman up front being like "hunting with a cat."
"Ancelotti is serenity," the 26-year-old told L’Equipe. "He doesn’t put pressure on the players. It is very different from Mourinho, who has another method.
"When it happened I thought, 'Why does Mourinho say that about me?' But everything is relative.
"There were no jokes about it back then but today my friends call me 'cat' and it is friendly. I am not a cat or a dog - there is nothing I can do!
"There were some difficult days, but I overcame them. Some people don’t know the difference between a good game and a very good game. If I produced a normal game, some observers would say I have been poor.
"At first, in the hard days, some mornings I would say 'I have no desire' but I could not afford to give up."
Benzema, who is often the subject of speculation surrounding his future, says he feels at home in Madrid and has been inspired to work harder by following the example of Ballon d'Or winner Cristiano Ronaldo.
"I am happy in Madrid. This is my home,” he added.
"I love working. After training I stay in the gym. I noticed this about Cristiano Ronaldo... I realised I should aim higher, like he does."