The problems on Saturday caused fans to miss both the opening ceremony at Soccer City and part of an historic rugby match in Soweto's new Orlando arena.
The kick-off in the South African Cup final at Soccer City was delayed by 30 minutes because of traffic congestion.
Callers to radio stations on Monday said they had been stuck for up to two hours in a jam on the off ramp from Johannesburg's urban motorway.
Johannesburg transport boss Lisa Seftel said a combination of problems, including two big sports events at the same time, road construction as part of World Cup preparations, and a rail strike caused the problems.
She told 702 Radio that construction delays would be over by the World Cup kick-off on June 11.
Soccer City has been completely overhauled and redesigned in the shape of a traditional cooking pot or calabash for the World Cup.
It is Africa's biggest stadium, with a capacity of more than 90,000 and will host eight matches, including the opening and closing games.
But the stadium was half empty when President Jacob Zuma cut a ribbon to open the arena near the township of Soweto, although it filled up by the time of the delayed Cup final kick-off between Amazulu and Bidwest Wits, which was won by the latter.
The game coincided with the semi-final of the Super 14 rugby tournament between Blue Bulls and Crusaders, the first top-grade game played in Soweto, heart of the anti-apartheid struggle.
"The lessons that we've learnt are really lessons in coordination and planning," Seftel said. .
"We probably didn't do enough to tell (spectators) about alternative routes. What we're going to do for 2010 (the World Cup) is that on the tickets, we'll tell people what route they must take to the park and ride."
