Despite going ahead through Dries Mertens, who equalled Napoli's all-time goalscoring record, the Serie A side was held 1-1 at home.
Antoine Griezmann levelled for Barca during the second half, although the LaLiga giant also had Arturo Vidal sent off late.
Gattuso said his team is ready for a battle at Camp Nou on 18 March.
"Nothing is over for us when we're playing the last 16 in the Champions League, not even when we play cards," the Napoli manager said. "We know the difficulties we are going through. We will buy helmets and armour.
"We will get all the necessary [tools] and will play the next game. Nothing is over."
While Mertens's brilliant finish gave Napoli a lead, a well-worked team move led to Griezmann's equaliser for Barca.
Gattuso lamented his side's defending for Griezmann's goal, but was largely satisfied with its performance.
"I am disappointed because we made kind of a mistake defensively and they hit us. For sure we could do better," he said.
"When Lorenzo Insigne had his chance [Arkadiusz] Milik and [Piotr] Zielinski were not marked. Perhaps we could have exploited that situation in a better way. Same applies for [Jose] Callejon.
"There is some disappointment, we suffered but the team did almost everything right from a tactical point of view.
"I am happy for this, perhaps we could have done better passing. This is the only regret."