Miki Roque died at the age of 23 during the tournament after losing his fight against cancer, and the defender's death put things in perspective for Vicente del Bosque's team.
Sevilla defender Antonio Puerta passed away in 2007, while Espanyol captain Dani Jarque died in 2010, and Fabregas was keen to remember those men in his hour of glory.
"I have a t-shirt with people who have left us, but will always be with us. We value life, especially right now. This is for the whole family. I hope they enjoyed it as much as possible in these circumstances," Fabregas stated to Telecinco.
The midfielder then stressed that the 4-0 victory over Italy was "huge" for Spain, and hit out at the people who criticised the European champions for their style of play.
"This is huge. The first goal put us in pole position, and we put in a great performance from then on. You always have to win a final, but it feels even better to do it like this.
"It feels really, really amazing. It's one of the best days of my life. I don't think we realise what we've done. But in time we'll realise what we've done.
"If somebody had told me this before, I wouldn't have believed that we would win 4-0. It was more difficult than it seemed. The match was effectively over when they were reduced to 10 men due to Thiago Motta's injury.
"Are we boring? People who think we are boring, I don't think they understand the game."
Centre-back Gerard Pique also had Miki Roque in his thoughts.
"We want to dedicate it to the family of Miki Roque. Miki, we are with you," the defender said to Telecinco.
The former Manchester United stopper felt the exit of Motta effectively ended the game for Italy, and went on to praise Spain's defensive performance.
"We didn't see as much of the ball as we wanted in the first half, but we still scored two goals. Things got a lot easier with Motta's injury.
"The entire team has performed well defensively. We were very good in defence, and it obviously helps a lot that we have so much creativity up front."