Borussia Dortmund's late winner at Marseille meant Napoli came third in Group F - due to an inferior three-way head-to-head record with the Germans and Arsenal - even though they finished with 12 points having won four of their six games.
No other side in Champions League history had accumulated such a haul and gone out - in contrast, Zenit St Petersburg advanced from Group G with just six points - and Argentina international Higuain struggled afterwards to understand what had happened.
"I can't believe we didn't make it," Higuain told sscnapoli.it. "To have been eliminated in this manner seems absurd.
"No-one else in the other groups have collected 12 points and not qualified.
"We have played a fantastic Champions League and we deserved to go through.
"The team has shown its true value and we want to continue like this.
"We will focus on Serie A and then we have the Europa League adventure to look forward to in February."
Napoli president Aurelio De Laurentiis believes his players left the competition with their heads held high.
"I have to compliment my players," De Laurentiis said.
"The team has proved to be at a high level and this gives me further confirmation that (Napoli coach Rafael) Benitez is doing a good job.
"We are growing and I'm sure with Benitez's play and with these players we will go far.
"Our project only just started and we will continue on this path.
"I told my players at the end of the game that they shouldn't cry but rather celebrate because they have played a great Champions League.
"They have honoured this jersey and they deserve everyone's praise."