Fabregas featured from the start in Kiev and crossed for David Silva in the 14th minute for La Roja's first goal of the night.
Spain are the first side to win three consecutive major international tournaments, but their approach to the game had come under criticism prior to the match and was labelled as 'boring' in some quarters.
"Those people who think we are playing boring, in my opinion they don't understand the game," he told BBC Radio 5 Live.
"This has been one of the best days of my life. Three major trophies in a row has never been done before in the history of football."
Despite the hefty scoreline, which represents the biggest margin of victory in a final in the tournament's history, Fabregas insisted that Italy had provided Vicente del Bosque's team with a stern test at the Olympic Stadium."If I had been told we would win 4-0, I would not have believed it," he admitted. "It was harder than it seemed.
"They were reduced to 10 men after Thiago Motta's injury and it was all over for them."
After the match, Fabregas paid tribute to Dani Jarque, Miki Roque, Manolo Preciado and Antonio Puerta, who have all passed away in recent years, by wearing a shirt with their names on it.
"I have this shirt with the names of the people who have left us but who will always be with us," the 25-year-old added.
"We really value life, especially in moments like this. We hope that their families will enjoy this moment in the best possible way."