Barcelona were beaten 4-0 in the Parc des Princes and needed a miraculous comeback in the return leg to book their place in the quarter-finals, with Sergi Roberto eventually rounding off a stunning 6-1 win well into stoppage time.
Luis Enrique's men now face Juventus, and Higuain thinks Barca will be brimming with confidence ahead of Tuesday's first leg in Turin.
"Football is so changeable, and a team that everyone thought was knocked out went through to the quarters. They will be full of confidence," Higuain told UEFA's official website.
"Barca had an off day [in Paris] and I do not think they will have another quite like that.
"We have home advantage first and want to get a good result to give ourselves a real chance in Barcelona.
"We will not be able to take our foot off the gas, not even for a split second."
"I hope we can win the Champions League. That is why I came here," the attacker added.
"We are also going for our sixth consecutive Scudetto and the Coppa Italia, all big targets.
"Winning six Scudetti in a row would be unprecedented; likewise winning the Coppa Italia for a third straight year would also be something no other team has achieved.
"Of course, the Champions League is a dream we want to make reality, but we cannot discount the other two."