The 24-year-old Spanish World Cup winner came on for Pedro in the 82nd minute, just after Real had equalised at 2-2, but Lionel Messi grabbed a late volley to give the European champions a 5-4 aggregate triumph.
"I'm very pleased. It's a great start winning and with such positive sensations," Fabregas told Spanish state television as Barca's players paraded the trophy around the Nou Camp.
At the end of Wednesday night's game, Fabregas, who had not had much chance to contribute to the action, was hacked down by Marcelo near the two dugouts.
A huge touchline melee between the Barca and Real Madrid squads ended with Marcelo, his Real team mate Mesut Ozil and Barca's David Villa all being sent off.
"Football is very competitive, they are two of the biggest teams in the world, and the rivalry is great," he added with a shrug.
"These are things that always happen in football."
