The former Everton man created both goals — an Alin Tosca own-goal and Sergi Roberto's strike — as Barca responded well to a difficult week.
The club had already paid tribute to the victims, at least 14 of whom have died, with commemorative shirts worn for the league opener, but Deulofeu felt a win was a fitting addition.
"We wanted to celebrate this victory for the victims," he said. "What happened was terrible. It is a special victory that we dedicate to those affected.
"Let's hope it stops already. We are not afraid, but it has to stop."
Deulofeu's place in the team is under pressure with reported moves for Ousmane Dembele and Philippe Coutinho in the pipeline, but the Spain international delivered in the absence of the injured Luis Suarez to help Barca home.
"I am satisfied, very happy. I have played a few games and can always improve," he said.
"I have to take risks a little more. I have come back from an injury and I have to give everything I have."
Goalscorer Roberto was pleased with his own contribution, too, as he looks to secure a regular place in midfield, having spent last season at right-back.
"I am happy. I played a good game at the Bernabeu [in the Supercopa de Espana second leg] and today I think I have also done a good performance," he said.
"I feel very comfortable in this position and hope to have more minutes with the coach. The coach is giving me confidence and that's what I want.
"I want to be important, it's the club of my life and now I'm fine."