A brilliant brace from Paulo Dybala set Juventus on their way to a crushing win, with a second-half Giorgio Chiellini header extending the Serie A leaders' advantage in Turin on Tuesday.
But Barcelona came from 4-0 down after their first leg against Paris Saint-Germain in the previous round, with Sergi Roberto's injury-time strike sealing a 6-1 victory to complete one of football's unlikeliest comebacks.
Alves said Juventus must therefore aim to score to increase the size of the task facing his former club when the sides meet again in Barcelona on April 19.
"I think that at the Camp Nou you cannot go to defend the result," the 33-year-old told Mega. "You have to go try to score, try to make it difficult for Barcelona and try to beat them.
"Our win had a lot of merit. Our effectiveness meant that Barcelona did not have spaces, they could not handle the game as they like and that is always a difficulty.
"It is difficult for opponents and we have to be cautious because something has already happened at the Camp Nou, where the games last a long time. Camp Nou is big and we will suffer, but we will score goals and pass the tie."
Alves played for Barcelona between 2008 and 2016, winning the Champions League three times during a trophy-laden spell, and the right-back said it felt odd to be facing his old colleagues.
"It was a strange sensation," Alves conceded. "I was happy but the sadness of my team-mates is also mine, so I did not celebrate the goal.
"I prefer to keep my happiness to myself in respect for the years I spent with them."