The South Americans continued to dictate terms after that and took the lead in the 20 minute when Philippe Coutinho curled a spectacular 22-yard effort into the top corner, 1-0.
As Brazil pressed forward early in the first half Coutinho picked up a loose ball at the edge of the 18-yard box and put his shot out of reach of Switzerland's goalkeeper Yann Sommer and in off the far post.
"Until we scored the goal there was a lot of pressure". There was a lot of anxiety, too much pressure and it translated into our way of playing, we were not precise enough.
"But the most important is that we have peace of mind so that we can recover well and go back to Sochi with our families to gear up for the next match".
In their first World Cup game since famously losing 7-1 to Germany in the semi-final in Rio four years ago, Brazil took their time to warm up.
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Tite did not complain that his side were denied a penalty when Manuel Akanji wrapped his arms around Gabriel Jesus and had little sympathy with claims some of his players had been fouled when Switzerland levelled.
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I'm here to enjoy my golf this week, to play freely. "This was a long one, definitely a bonus", Johnson said. In terms of scoring, it was the second easiest of Shinnecock's 12 par-4 holes on Thursday.
Brazil may point to a push by Zuber to free him from his marker but the fact Coutinho's strike remained their only effort on target until 77 minutes points to their struggles in the final third.
"I am proud of their determination", Petkovic said of his team. "You can interpret the penalty in any way but there's no way you can complain", he added.
Tite said he wouldn't make excuses for the disappointing scoreline.
In a World Cup where sides have shown promise without being scintillating, Tite and the passionate Brazilian public are unlikely to be too anxious at this stage, and Switzerland are after all the world's sixth-best side on ranking.
Meanwhile, Tite's opposite number Vladimir Petkovic said he hoped his team would get some deserved recognition for the hard-earned point after few had given Switzerland a chance against one of the favourites in Russian Federation.
"I am very proud of my team's discipline, it was everything we talked about", he said. "Sometimes there is a lack of recognition (in Switzerland's ability) and I think that's a pity because this team really believes in itself and can achieve results". "We got a draw but this is only the beginning for us". But we can improve, we can play better.
Switzerland have lost only one out of 12 competitive matches since Euro 2016 - a World Cup qualifier away to Portugal.
"I spoke to Miranda and he said, "When he pushed me I should have fallen" and I said: 'No!"