Rafael Benitez's men missed out on the last 16 due to an inferior goal difference, despite their 2-0 home win over Arsenal in their final Group F fixture on Wednesday.
Gonzalo Higuain and Jose Callejon scored second half goals as Napoli saw off Arsenal to finish level on 12 points alongside both their visitors and Borussia Dortmund, but they will play in Europe's second-tier went out due to their inferior goal difference.
With Dortmund drawing 1-1 in Marseille going into the final three minutes, Napoli looked to have sealed qualification, only for a Kevin Grosskreutz winner in France to dash their hopes.
After the match De Laurentiis claimed that they will look to triumph in the Europa League, despite his misgivings in previous years.
"There is not bitterness," he said.
"You know that I never gave importance to the Europa League, but this time we enter from the group of the death and will be different.
"This was an extraordinary group and we have a great coach who knows how to transmit his ideas."
Benitez, meanwhile, said his side deserved to go through after they became the first team ever to go out of the competition at the group stage having amassed 12 points.
"The team gave its all and deserved both to win and qualify," he said.
"But that's football. I think they key is to look at this as a stage during our growth process and proof we are on the right track. The fans and everyone should be proud of what Napoli have achieved.
"The Europa League doesn't start until February, so we'll think about Serie A for now."