Haggui was part of the 2004 team that lifted the title on Tunisian soil.
The latest version of the Carthage Eagles with its mix of veterans and new recruits began its quest for a second crown by winning Monday's opening Group C game against Morocco.
That 2-1 victory put them second on goal difference behind table toppers Gabon, who opened with a stylish 2-0 win over Niger.
Hannover 96 defender Haggui said: "We deserved to win as we played a really good game. Tunisia's new generation wants to write its own history and looking at the potential of these young players that we've got I really hope we can write it at this Nations Cup."
Tunisia downed Morocco with goals in either half from Khaled Korbi and second half substitute Youssef Msakni, with Houssine Kharja getting a late consolation for Morocco.
Tunisia coach Sami Trabelsi described his team's performance as "heroic".
"It's a precious win, which is going to help us in our journey during this Cup," he added.
"We were up against a technically very good side but my men were excellent on the level of tactics and the aggression they showed.
"Without our spirit and aggression we wouldn't have won.
"But the competition is long, it's just one win and we have more matches to come. I hope we can qualify."
Tunisia are next up against minnows Niger, brushed aside by the co-hosts in chilling fashion in Monday's first game at Libreville's L'Amitie stadium.
Looking ahead to Friday's clash with the Cup debutants Trabelsi added: "Our preparation for Niger starts now, this game is more important than Morocco."
Morocco captain Houssine Kharja was far from disheartened, believing his team, who meet Gabon also on Friday, could still make it to the quarter-finals.
"We still have two matches to qualify, I believe we have what it takes to make it."
His coach, Eric Gerets, identified a period in the second half when his team "lost their heads and played with their hearts" resulting he said in Tunisia's second goal.
"For nine or ten minutes we forgot our tactical organisation and that's why (Tunisia) were able to score.
"With a little bit of luck we could have come away with a draw, that would have been fairer than zero points.
"For 20 minutes in the second half I believe my team showed why we qualified, we played very good power play football.
"This Cup can produce surprises, that's life."
Looking ahead to the date with Gabon he commented: "The next match is an all or nothing affair. We've got more pressure on us now."
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