The full-back gives credit to his former side, admitting that the league leaders were forced to put in considerable effort to seal the victory at Camp Nou
David Villa and Lionel Messi both scored following Alberto Botia's first-half strike for the visitors, as the Blaugrana extended their lead at the top the table to 15 points over Atletico Madrid, who play on Sunday.
Speaking after the game, Alves revealed that he was satisfied with the Catalans' reaction to going behind and also praised the visitors' resolve.
"It was a strange match especially because of how cold it was, but in the end we managed to win," the 29-year-old Brazilian was quoted by Mundo Deportivo.
"Sevilla forced us to work hard to win the three points. They are not just any team, they are great rivals and have a lot of quality."
Alves played 186 times for Sevilla before moving to Barcelona in 2008 and, while he was quick to praise los Rojiblancos for their effort, he was also critical when asked about his side going into half-time 1-0 down.
"We have to improve in this regard," the Brazil international confessed.
"But we can concede goals if we win. This is a game and we have to remember that other teams are also playing. We reacted well and we deserved the win.
"It’s an important week, and that’s how we're approaching it. These are the types of matches that we like to play," he added, referring to Tuesday's Copa del Rey semi-final clash with Real Madrid.
Barca have now amassed 68 points from their 25 league games this season.