Lionel Messi proved the matchwinner for Sunday's 1-0 triumph.
"It isn't decisive, however this victory is significant to the league table," said Alba.
"They pushed us much more in the second half. If we had failed to win, the points difference would have lessened."
Atletico coach Diego Simeone made clear after the match that the only difference between the two teams was Messi himself, with left-back Alba quick to praise his teammate.
"Simeone hasn't stated something new, Messi is the best, but we must highlight the work of the team.
"Messi wins games but, without the work we all do, he wouldn't be able to do so."