Giaccherini started for Italy at Craven Cottage and struck the equaliser for a 2-2 draw to ensure the Azzurri avoided defeat in their last game of 2013.
"I am delighted with my performance and that of the team," Giaccherini said.
"It's a pity that just when we were playing at our best, Nigeria scored twice.
"I think in any case we reacted well and we were able to draw.
"We really wanted to do well in our last friendly and I think we handed a good performance."
Italy went through qualifying unbeaten and sealed a spot in next year's tournament in Brazil with two games to spare.
"I believe that when the important games begin Italy will be ready," Giaccherini said.
The 28-year-old Giaccherini has scored two goals in eight Premier League appearances for Sunderland this season.
"I just hope to continue to do well and conquer a place for the tournament in Brazil," he said. "I know that we are at least 30 players that are fighting for a World Cup spot and we will to fight until the end in order to earn a spot in Cesare Prandelli's final squad."
Italy will play their last international friendly against World champions Spain in March 2014 prior to travelling to South America.