The Carthage Eagles and Cape Verde shared the spoils in their opening game of the 30th edition of the continental showpiece, at the Nuevo Estadio de Ebebiyín.
Debutant winger Mohammed Ali Moncer was on target for Tunisia while Cape Verde equalised courtesy of Heldon Augusto Almeida Ramos.
The 65-year-old mentor believes that Group B is wide open for any team to win it, but has also said that the 2004 winners will be going full-out to grab the maximum points in the remaining two matches against Zambia and Democratic Republic of Congo (DRC).
“We are not the favourites to win our group,” said Leekens.
“We have never said we are going to top the group.
“We had lot of problems coming to this match (against Cape Verde).
“Usually, we don’t play the way we played tonight (Sunday).
“We had two players in our starting line-up who were making their debuts.
“This meant that we were forced to find our rhythm as early as possible.
“It was not easy at all because first games are always difficult to play in competitions like these because you really don’t know how your opponents play.
“But I believe that we didn’t deserve to lose this game and we’ll be more focused on the next two games.
“At this stage, every team in the group is the favourite to finish on top.”
Tunisia will face Zambia in their next game on Thursday.
Kick-off is at 18:00 (SA time).