The Warriors were drawn in Group B alongside seven-time champions Egypt, Angola and South Africa at the tournament, which begins in Morocco on 21 December.
Zimbabwe open their campaign against Egypt on Monday.
“We are going there to compete,” Nakamba told South African broadcaster SABC Sport on Thursday.
“I think we just have to believe in ourselves and give everything, with the support of the new guys in the team.
“Football is about competition. Every group is tough,” he added.
“We are playing Egypt first, then Angola and South Africa, but we just have to focus on ourselves.”
The Luton Town midfielder dismissed suggestions that recent changes to the technical staff had unsettled the squad, saying the mood in camp was positive.
Romanian coach Marian Marinica was appointed Zimbabwe’s new head coach in November, replacing a German coach who failed to register a win in six World Cup qualifying matches.
“So far, so good. We are pushing each other in camp, the morale is high and everyone is focused. Hopefully we can go there and achieve something positive.” Nakamba concluded.
Zimbabwe have never progressed beyond the group stage of the Africa Cup of Nations.
They will make their sixth appearance at the tournament in Morocco hoping to end that run and reach the knockout rounds for the first time.
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