Drawn alongside England and USA, no-one has given the team any chance of progressing to the knockout stage. Slovenia, a country of only two million people, are the smallest nation at the FIFA World Cup™ but that does not deter Kek or his players.
"We are facing a daunting challenge. We are not favourites but it is our desire to win every match," said the manager. We will do our best to show how good Slovenia is and I am very happy that my squad is very motivated and keen to tackle the challenges they face. Irrespective of the result tomorrow, if we do our best and leave our hearts out on the pitch I will be very proud of them."
Although Slovenia have yet to win a match in the two major tournaments they have played in - UEFA EURO 2000 and the 2002 FIFA World Cup - they showed their quality in an impressive qualifying campaign.
They finished just behind Slovakia, ahead of Czech Republic, Northern Ireland and Poland and beat Russia in a two-legged play-off to reach South Africa. Kek's side also made things difficult for England - who they will meet in Port Elizabeth in their final group match on 23 June - in a 2-1 defeat at Wembley in September.
And, despite being written off as cannon fodder for England and USA, the Slovenia boss said the qualifying campaign in which they conceded just four goals in 10 games - bettered only by Netherlands among the European teams - had given them confidence.
"These figures are very positive," Kek added. "Any World Cup is a challenge. This does not present any pressure for us. It is another challenge, another motivation."
Kek said he felt the squad was a tight unit, unlike in South Korea and Japan eight years ago when Zlatko Zahovic, Slovenia's star at the time, had a major bust-up with then manager Srecko Katanec after the first match and was sent home.
"I am glad all the players are confident," said the 48-year-old. "There is no room for fear, anguish or pressure because we have done our best so far and we can only gain from this World Cup. I expect a decent match and I believe both teams will be seeking to win because the first game is very important in terms of the tournament and important for confidence."