The Spain international netted a consolation goal in the Blaugrana’s 3-1 defeat to Jose Mourinho’s men at Camp Nou on Tuesday, which saw them eliminated from the Copa del Rey.
"If I score at the Bernabeu, I would go nuts!" he told DiR.
With coach Tito Vilanova receiving cancer treatment in New York City, Barca has not been at its best in recent weeks, but Alba was quick to stress that it is still fighting hard for the 44-year-old.
"Tito is a great person, he’s very humble, but he's fights as hard as they come and we hope to have him back as soon as possible,” he added.
"We fight for him and for all of Barcelona. When we win, our victories are devoted to him."
Alba rejoined the Camp Nou outfit at the start of the season after leaving the club as a child, and he went on to admit that he never thought he would get the chance to represent the Blaugrana again.
"When I left La Masia at 16, I thought my time with Barcelona was over," he continued.
"At first I struggled a bit [on my Barca return], because I caught the flu and was pretty ill for two weeks, but after playing against Sevilla, everything went fantastically well and now I'm having a very good time, I feel great."
The full back also defended Lionel Messi, who has been criticized in the past few weeks after failing to make an impact in the losses to Madrid and AC Milan.
"There are players that make a big difference in [modern football], but no one else is as good as Leo," he added.
"He's a pleasure to have as a teammate, and he has treated me very well from the beginning, with great humility, and on the field he keeps proving he is the best."