The Taifa Stars are returning to the tournament for the first time since 1980 and will begin their campaign against Senegal at the 30 June Stadium in Cairo on Sunday.
Paired along with the Terenga Lions - ranked as the best African side in the latest Fifa ranking - North African giants Algeria and Kenya in Group C, Amuneke is confident his side will match their opponents in the tournament.
"The most important thing for us is to be part of this competition. We come back after 39 years,” Amuneke said in his pre-match press conference.
“We are aware that Senegal are one of the strongest teams in Africa, individually and as a team. But I also believe if you are in such a tournament you have to believe in yourself. We have to be in a position to compete.”
After their outing against Aliou Cisse’s men, the East Africans will lock horns with neighbours Kenya on Thursday before slugging it out with Algeria in their last group game on July 1.
The Taifa Stars suffered an embarrassing 7-0 defeat to the Desert Foxes in a World Cup qualifying game back in 2015.
However, Amuneke who has improved the team since taking charge last year has sent a strong warning to the North Africans ahead of their meeting.
“There is no doubt about the quality of Algeria. We know we were hammered 7-0 three years ago, but the Tanzania of that time is not the one of today.”
Tanzania will look to forward to a favourable result against Senegal to boost their chances of qualifying for the knockout stage of the tournament for the first time in their history.