Former captain Maurice Odumbe called for Kenya to be awarded Test status on Saturday, after the tournament minnows joined Australia and India as the first three sides to qualify for the World Cup second phase.
The 33-year-old Odumbe, voted man of the match after Kenya beat Bangladesh by 32 runs in Group B at The Wanderers, said: "We want to play Test cricket and we don't mind being with the big boys."
Odumbe, who top-scored with a 46-ball 52 not out and took four for 38 in 10 overs, added: "The Kenya (cricket) association has been lobbying very hard for test status. I don't know how far along it has gone but I definitely believe we belong there.
"Initially we will struggle but, unless you are put in that position, you will never know.
"A few months ago we almost knocked off Australia," he added, referring to Kenya's five-wicket defeat by the world champions in Nairobi last September.
"It takes only 10 good balls and voila -- things change. We have to be optimistic."
The Kenyans, professional players contracted to their national board, carried three years of disappointment into Saturday's game, with Test status having been awarded to Bangladesh ahead of them in 2000.
Kenya, who have now beaten Bangladesh in six of their seven one-day meetings, had argued they should have become cricket's 10th Test-playing
Odumbe is determined that Kenya compete in the Super Sixes.
"We can't go into the Super Sixes with a defeatist attitude," he said. "We are here to compete and we will compete.
"If we beat South Africa or another team, it doesn't matter. We don't mind. A win is a win, even against a team like Canada. This is the World Cup, not a village tournament."
Kenya, who already have one-day status, recorded their first World Cup win with a shock upset of West Indies in 1996.
They have won four of their five group matches at this tournament -- one a forfeit after New Zealand refused to travel to Nairobi over security concerns -- and head Group B on 16 points with Sri Lanka who are yet to qualify.