South Africa, who sent their supporters wild when they took the lead through Siphiwe Tshabalala's superb 55th-minute drive, were pegged back by Rafael Marquez's equaliser in the 79th minute. The Bafana Bafana then came agonisingly close to sneaking a win right at the death when striker Katlego Mphela hit the post after outpacing two defenders.
But Parreira said he thought the draw at Johannesburg's Soccer City stadium was a fair result and after seeing his side grow in confidence as the game wore on, said his team are now set up in their bid to qualify from Group A.
"As the game progressed, the players became more relaxed and I think the players have broken the ice in terms of playing in a competition like this," said the Brazilian. "The draw keeps us alive in the competition."
Parreira said the game had been a balanced affair, but although the Mexicans had a lot of possession, especially in the first half, they could not find the net. "We knew this team, they are one of the most daring teams in the World Cup with two strikers and two attacking fullbacks, they are very enterprising," he said.
"I believe we were more balanced in the second half and could have won the game. We are still in the competition. It is a fair result, I can't ask more from the players, I think this group is very tough. The spirit was high from the beginning. Whatever happens we are still in the group and I expect it will be decided by the last game against France."
And the Brazilian praised his players for the way they coped with the pressure from a crowd of nearly 85,000. "That was a lot of pressure for my team out there. It is really hard to play well in front of around 90,000 with so much expectation upon you."
Parreira, who took his native Brazil to a FIFA World Cup triumph in the United States in 1994, praised the passionate crowd, who created a wall of deafening noise with thousands of vuvuzela trumpets blowing throughout the game. "The support for us was very good and has been all along," he said.
When asked why talisman Steven Pienaar was substituted towards the end of the match, Parreira said the Everton midfielder had struggled with cramp. "Pienaar seemed to be struggling in that supporting role towards the end. He was having a little cramp and he has played 45 games this season and didn't have so much time to be prepared with us."