Kek, who steered the Slovenians to their second World Cup finals after a group stage appearance in 2002, believes team spirit will outweigh a lack of world class talent in the squad for the South Africa tournament.
"We have no outstanding players but our team spirit is second to none and it guided us through the qualifiers to the World Cup," he told Reuters by telephone on Tuesday.
"We would achieve historic success if we reach the last 16 in South Africa and I have faith that we can do it, although our preliminary round (Group C) is tougher than many people think.
"England are obviously one of the tournament favourites but the United States and Algeria are not to be underestimated either, especially the latter because they will be playing in their home continent.
"South Africa will be uncharted territory for most teams and it may give African teams an edge while the top teams face stern tests of their credentials every step of the way."
The Slovenians qualified for Euro 2000 and the 2002 World Cup after gaining independence from the former Yugoslavia in 1991 but the brightest spell in their soccer history precluded an eight-year exile from the big events.
Qualifying for a major tournament was always going to be a tall order for a country of just two million, where the local league is devoid of quality and usually takes a back seat to winter sports.
FAVOURITE SON
However, the current crop of players delighted their home fans by upsetting Russia in one of Europe's four playoffs to reach the finals and Kek believes the best is yet to come in South Africa.
"I can't say if any of our players will stand out in our bid to impress because that would be like picking a favourite son, they work for each other and everybody works for the team and that's our greatest strength.
"We have several prospects who are making good progress at their clubs and are very likely to make the final 23-man squad, namely (Inter Milan midfielder) Rene Krhin and (Groningen sriker) Tim Matavz.
"It is essential that everybody stays fit ahead of the World Cup and if that happens we have a good chance of advancing from our group into the knockout stage."
Kek believes there are more candidates than usual to lift the World Cup trophy but does not expect any single player to grab all the headlines in what should be an enthralling month-long tournament starting on June 11.
"We have the usual suspects for the title and more dark horses than ever, while teamwork will be vital because it is difficult to expect any one player to outshine everybody else.
"Lionel Messi is yet to emulate his Barcelona form in an Argentina shirt, while (Portugal's) Cristiano Ronaldo and (England's) Wayne Rooney will be under a lot of pressure and need their team mates to perform."
