The Barcelona left-back struck twice in Sunday night's victory in Fortaleza as the world and European champions ensured they finished top of the pool, and in the process doubled his international tally.
He told FIFA's website: "This is clearly new to me, particularly because of the quality of the forwards in this squad. If it's odd for me to score just one...
"Of course I'm pleased, but I'm also happy we kept a clean sheet and beat a team like Nigeria, who made life difficult for us for the whole 90 minutes."
Alba's first senior goal for his country came in last summer's Euro 2012 final, when he scored the second in their 4-0 triumph over Italy.
The two sides will meet once again in Thursday's semi-final, although the 24-year-old is not sure there will be a repeat this time around.
Alba said: "That goal was special because of everything it meant, but to start thinking about scoring against them again...
"For now, I'll just savour these two goals. That's enough for me."
Striker Fernando Torres, who found the back of the net in between Alba's third and 88th-minute efforts, was full of praise for his team-mate.
He said: "A lot of people saw him as a player who had come out of nowhere, who from one moment to the next carved out a spot for himself.
"Everyone was really impressed with him at the last Euros, perhaps because they had not seen him play for Valencia. Now you watch him at Barcelona and it looks like he's been playing with them for 10 years.
"He's getting more influential all the time with La Seleccion too."