A false start to the season saw the Blaugrana win just four games in their opening 12 La Liga matches as Real Madrid took a healthy lead.
Barcelona have only lost twice since Xavi Hernandez's appointment in November which has seen them climb up the table to second position.
Pierre-Emerick Aubameyang's 11th minute strike gave Barcelona a 1-0 victory over Real Sociedad on Thursday, cutting Real Madrid's lead to 15 points.
Although Barcelona have one game in hand, Los Blancos have almost certainly claimed the La Liga title as they need just four points from their remaining six games to be crowned champions.
Barcelona defeated Real Madrid 4-0 last month to underline their improvement under Xavi and Alves is adamant a better start to the season would have produced a tighter title race.
"Lucky for them [Real Madrid] we haven't arrived earlier," Alves told Movistar+ post-match.
"We always plan to compete differently but in the end, life is like that. We arrived late and had to make a tremendous effort to take the advantage over them.
"We already knew it was very difficult due to the state of the rival and the situation, but I insist, lucky for them that we have not arrived earlier."
"We knew it was going to be difficult, because it's always very difficult here," Alves said. "The stadium is very tight, we controlled a little more in the first half and then we lowered the intensity but you have to know how to suffer. In football it's hard to win, but you win.
"We wanted to balance the team a little more and the goal came and decided the game. You have to know how to suffer to win games."
