Higuain scored in Napoli's 2-0 win over Premier League leaders Arsenal on Wednesday but it was not enough for Rafael Benitez's men.
Despite winning four of their six Group F matches, Napoli failed to qualify, finishing third on their head-to-head record.
It was the first time a side has failed to reach the next stage with 12 points and Argentina international Higuain was devastated.
"It cannot be anything else but bad luck, because to win four games out of six and be eliminated is not something that happens often," he said.
"Not going through is incredible. It is an injustice, really.
"Going out with 12 points - winning four games in such an immensely difficult group with two sides as strong as Arsenal and Dortmund - when you see teams going through with only one or two wins, with six or seven points, it's disappointing."
Higuain has now set his sights on winning the UEFA Europa League, a trophy that manager Benitez lifted last season with Chelsea.
The forward, who scored four goals in his five Champions League matches this term, added: "Now we've got to look forward to the Europa League, Serie A and the Coppa Italia.
"Our aim now is to win the Europa League. It's a trophy and it is very important for us."
