The Naples outfit ousted Roma from the Coppa with a 3-0 triumph on Wednesday to win 5-3 on aggregate and set up a meeting with Fiorentinain the final on May 3.
"We are delighted," Higuain said to Gazzetta dello Sport. "This is a game to remember.
"We deserve to be in the final and we beat a very strong Roma.
"Our aim was to reach the final and we have succeeded but we are not going to settle just for this.
"Until it's mathematically impossible, we will continue to battle for the Scudetto.
"We know it's going to be difficult.
"Juve are 13 points clear but we will continue to fight and try to to surprise everyone."
Napoli are third in Serie A and hold the last Champions League qualifying spot to trail four points behind Roma, who are second and have a game in hand.
Napoli travel to Sassuolo on Sunday while Roma take on Sampdoria at the Stadio Olimpico.
Serie A leaders Juventus are at home this weekend to square off against Chievo.
The Turin giants were held to a 2-2 draw at Hellas Verona last time out but remain nine points clear of nearest rivals Roma.
Inter Milan ended a five-match winless run with a 1-0 triumph over Sassuolo last time out but take on a Fiorentina side on Saturday that has its confidence sky-high.
The Viola beat Udinese 2-0 on Tuesday to progress to the Coppa final.
Fiorentina are fourth, three points adrift of Napoli.
AC Milan are the only Italian team alive in the Champions League and they will take on Atletico Madrid in the European competition next week.
Before that, Clarence Seedorf's men will look to bounce back from last weekend's 3-1 loss at Napoli when they take on Bologna on Friday.
Lazio coach Edy Reja has yet to lose since replacing Vladimir Petkovic at the start of the year.
The Biancoceleste travel to Sicily to face bottom-side Catania on the back of a goalless result in last Sunday's derby against Roma.
Hellas Verona and Torino will battle it out at the Marc'Antonio Bentegodi stadium on Monday knowing that a win for either side would see them take a giant step towards securing Serie A football next season.
Udinese will look to put their Coppa disappointment behind them and focus on clinching their third straight league win when they take on Genoa at the Luigi Ferraris stadium.
In-form Parma are riding a 12-match unbeaten run but will be put to the test in Bergamo with rivals Atalanta having fallen just twice at home this season.
Victory on Sunday at Cagliari would see Livorno climb out of the relegation zone provided Chievo lose at Juventus this weekend.
Livorno are 18th in the standings, one point adrift of Chievo, who hold the last position of safety.