Alves, 38, came on as a second-half substitute at the Santiago Bernabeu as Barca ended a run of five straight losses against Madrid in all competitions.
"The scoreline was a let off for Madrid," Alves told Mundo Deportivo. "I think 6-0 would have been fairer, although I must admit 4-0 turned me on. It was a real hammering!"
Alves returned to Barca for his second spell at the club earlier this season after six years away.
During his first period at Camp Nou, he was involved in 6-2 and 5-0 wins over Madrid, but he says the latest victory was special because it signals that Barca are on their way back after some difficult years.
"I've experienced historic moments against Madrid," he added. "This time was special because it was a sign that we're returning.
"Barca are competing again and the fans are excited. Respect had been lost [for] the club, but now everyone knows we're a competitive team."
Barca were ninth in the table as recently as November but have climbed to second under Xavi Hernandez, who replaced Ronaldo Koeman earlier this season.
Alves credits Xavi, his former teammate at Barca, with the turnaround and the dismantling of Madrid last month.
"I said 10 years ago Xavi would be [Pep] Guardiola 3.0," Alves said. "Because of how he understands the game, how he adapts his football to current needs and because he knows the club. He knows what is necessary here.
"It's the first time at Barcelona I've worked so hard on the physical side of the game. Xavi's secret is hard work. You have to fight.
"Guardiola had a lot of good [players] and we didn't have to run up and down. We won a lot of balls back in the opposition half. Now, sometimes we have to run and, for that, we need to be in good shape. We can't get by now on the work we did before because the game has changed a lot."
Alves also spoke about potential signings, saying he "would spend a lot of money on [Kylian] Mbappe, but not [as much] on [Erling] Haaland," and confirming the club have sought his opinion on Ajax winger Antony, who he played alongside at Sao Paulo. "I am not pushing [to sign Antony] but I have spoken about him [with the club]," he said. "If they ask me, I speak about players from my point of view. I have played with him, seen him grow and then move to Ajax, where he's shown how great he could be."
Speaking on Saturday at a news conference, Barcelona coach Xavi joked that he could "forgive Dani Alves anything" after the player's comments about Mbappe and Haaland
Xavi, who has previously refused to deny meeting with Haaland in Germany, laughed off Alves' comments at the same time as admitting a deal for the striker could be too expensive for Barca.
"The financial situation is difficult so let's see how we can do things," the Barca coach said. "We're planning for next season, but the financial situation is not easy.
"As for Dani, I can forgive him for anything, whatever he says. Sometimes [the media] complain that there aren't any headlines, but with Dani it's difficult to choose just one. He's a phenomenon, a leader."
Alves is out of contract at the end of the season but hopes Barca will give him one more year to help him secure his place in Brazil's 2022 World Cup squad.
"No one has said anything to me [about staying]," he said. "Now it's not about the youngsters showing they're good, it's about the older players proving they can still play at Barca and aren't out of fashion."