"We knew that set pieces were our forte", said Kolarov, who now plays for Roma after a stint with Manchester City.
In midfield, Valon Behrami was relentless in his pursuit of Neymar, keeping the PSG superstar subdued for large periods of the game.
Earlier, Serbia beat Los Ticos 1-0 to move to the top of Group F. Coutinho had been handed a central role behind Neymar, on his first competitive game for four months, Gabriel Jesus and Willian in a line-up filled with attacking intent.
Steven Zuber, a midfielder for Hoffenheim, equalized for Switzerland in the second half, heading home a goal off a corner kick in the 50th minute.
"I was expecting to get a victory so, of course, I'm not happy with the result", continued Tite.
But as numerous World Cup favourites have found so far in Russian Federation, friendly performances mean little when the competition kicks off for real and Brazil were found wanting against an aggressive and well-organised Swiss side.
Brazil went all out in pursuit of a victor and came agonisingly close to finding it but had to settle for a point and joined fellow tournament favourites Germany, Spain and Argentina in failing to win their first game.
"I was a little bit anxious about the referee", said Arsenal full-back Lichtsteiner.
And deep into stoppage time Schar's outstretched leg turned a goalbound effort from Silva wide as Switzerland held out for a vital point.
Still, despite all their possession the European side could not create any significant goal scoring chances and entered the half time break trailing by a goal.
"I hope that people will take notice of us and take us seriously, sometimes there's a lack of recognition and that's a pity because we played very well", SwitzerlandcoachVladimir Petkovic told reporters.
"We have a lot of great players in the national team and each one of them has his own responsibility", Coutinho said.
Neymar had another chance to redeem a rather forgettable performance in the closing seconds when Brazil were awarded a free-kick just outside the Swiss penalty box. "If everyone does his job, then the team grows and plays well". If we were a bit more concentrated, we could have made the goalkeeper work a little more given the number of attempts we had.
"It's hot. But we're not looking for excuses, ' Lichtsteiner said". I didn't see any bad fouls and there were too many yellow cards.