Everton midfielder Pienaar admitted Bafana Bafana struggled at the start of the match at Johannesburg's Soccer City stadium in front of a crowd of nearly 85,000 raucous fans clad in green and gold.
"It was the first game, the opening game and it's normal that there's a lot of pressure," said Pienaar, who added that South Africa got into their stride midway through the first half when they started playing their own game.
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The midfielder said that on the strength of the South Africans' second-half performance "we deserved the victory".
"I'm happy with the way it went. The first 20 minutes we were a a bit nervous. It's normal because if you look at our team it's only Aaron (Mokoena, the captain) who's played in a World Cup," he said.
"For the other 10 players it was our first game in a World Cup but we're quite satisfied with the way it went.
"We just have to go on and we can only get better now. We played against one of the best teams in the world and to walk away with a point, I think we must be proud of ourselves."
South Africa, who sent their supporters wild when they took the lead 10 minutes into the second half through Siphiwe Tshabalala's superb 55th-minute shot, were pegged back by Rafael Marquez's strike in the 79th minute.
The hosts then went agonisingly close to sneaking a win right at the death when striker Katlego Mphela hit the post after outpacing two defenders.
Pienaar welcomed the backing of the crowd, who kept up a deafening wall of noise with vuvuzela horns blaring throughout the match.
"I'm really proud of the fans for their support and I really appreciate it."
Pienaar was substituted towards the end of the match with coach Carlos Alberto Parreira explaining the Everton midfielder had struggled with cramp.
South Africa next face Uruguay in Pretoria on June 16 and then France in Bloemfontein on June 22.
