Kek and his players are desperate to beat Algeria in Sunday in Polokwane to set their tournament off to a positive start - and dump a major competition record they would rather not have.
In the previous major tournament finals they have reached, Euro 2000 and the World Cup of 2002, the Slovenians have not notched a single victory in six attempts.
That dismal record appeared to weigh heavily on Kek on Saturday as he rubbed his head nervously while the players jogged around the pitch.
His earlier bust-up with his technical team was not discussed.
PAST FLOPS
He rejected suggestions, however, that Slovenia's major tournament past flops were uppermost in his mind or that his team were running scared in Group C which also includes England and the United States.
"This does not present any pressure for us - this is a challenge and another motivation for us," he said.
"There's no room for fear, for anguish or pressure because we've done our best so far and we can only gain from this World Cup."
On paper, Algeria, ranked 30th in the world against Slovenia's 25th, do not present the toughest of challenges at a competition which pitches the leading 32 teams in the globe against each other.
Kek was certainly not taking them lightly on Saturday, though.
"Algeria have shown how experienced they are and this means that we are facing a daunting challenge," Kek said.
"Irrespective of the result, if we do our best and leave our hearts on the field of play I will be very proud of them," he added.
