Woolmer also told Reuters by telephone that he feared Shaun Pollock's side would not reach the second round.
"My gut feeling is not very good at the moment. I'm hoping they sneak through," he said. "The team are so tense. You can see it in the body language, their faces and their play.
"The media have built them up, and built them up, and built them up as the first hosts to win the World Cup."
South Africa, the pre-tournament second favourites behind champions Australia, have lost two of their first three games against West Indies and New Zealand, courtesy of centuries by Brian Lara and Stephen Fleming.
They already need other results to go their way as well as to win all their remaining games to reach the Super Six stage.
The team has been widely criticised in the media, with skipper Pollock and fast bowler Allan Donald the prime targets.
"It doesn't look like it at the moment but South Africa are hard to beat at home," Woolmer added. "They have to understand that and get stuck in and not worry about the Super Sixes.
"They have to try and relax and enjoy their cricket."
NO RESPONSE
Woolmer said New Zealand and West Indies deserved credit for their wins.
"They have done their homework and come hard at them. At the moment, there has been no response.
"It may sound harsh, but I feel South Africa have not got better -- they've stood still. It looks as if they are playing the same way as they used to, but with a team which is not as experienced or probably as good as it once was."
Earlier South Africa batsman Gary Kirsten had defended Pollock's captaincy, saying : "I don't think you can single out individuals -- certainly not the captain -- for a lack of performance... It's all of us to blame."
He spoke out after team mate Herschelle Gibbs suggested that the side were missing the leadership skills of former captain Hansie Cronje.
Kirsten responded: "I certainly don't feel that. This team has done exceptionally well in tournaments since Hansie's cricket was over."
UNDER FIRE
Donald, the only South African to take 300 test wickets and named by cricket bible Wisden as their second-best one-day bowler of all time, also came under fire on Tuesday.
Former South Africa all rounder and team mate Adrian Kuiper told The Citizen newspaper: "The bowling attack hasn't gelled and Allan Donald hasn't been a real threat, has he? I think it could be the end of the road for Donald.
"There comes a time in everyone's career. He isn't bowling with confidence and is only at half pace." Donald is due to retire after the World Cup.
One of the country's leading newspapers echoed Woolmer's advice on Tuesday, though in cruder terms.
The Johannesburg-based Star suggested the team should "do what the rest of the country did on Sunday night" and "get hammered on beer and wine and leave the regrets in the bottom of the bottle".
The Star said Australia had come back from a similarly poor start in 1999 to win the trophy, before repeating its suggested solution. "Beer -- it's the fuel of all champion teams," it said.
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