The 43-year-old praised his side for securing an injury-time win over the hosts, and also gave his view on the controversial red card handed out to Gary Medel
Piotr Trochowski and Alvaro Negredo put the hosts' ahead, before a double from Cesc Fabregas and a stoppage time winner from David Villa earned victory, with Gary Medel sent off for Sevilla.
Vilanova insisted that the victory was deserved, and opined that the comeback spirit shown by the team is testament to their mental ability to keep on winning.
"A draw would not have been the fairest result," the 43-year-old was quoted as saying by the club's official website.
"[We] created enough chances to win the game. It would be better to not suffer, but it's important to have the ability to sacrifice yourself in order to continue competing.
"This is what my team did throughout the match. A team that fights back proves that they want to keep on winning."
Vilanova also spoke about Alexandre Song's match performance and the controversial red card shown to Medel for an incident involving Fabregas.
"We've asked a lot of him [Song] lately because he was forced to play in a three-man defence, I think he played a great game." he added.
"If a player head butts an opposing player, it's a red card. The referee followed the rules. I'm puzzled by him [Mateo Lahoz, the match referee], what most would consider to be a foul, he doesn't."
Barcelona travel to Lisbon to face Benfica in the Champions League in midweek.