Defending champions Germany lost to Mexico on Sunday while Argentina were held by Iceland and Spain drew with Portugal, with only France of the fancied teams winning despite an under-par display against Australia.
However, the Brazilian script was unravelled as Steven Zuber headed home a corner cross to level the playing field. Costa Rica, so far, has none.
The stalemate left Tite unimpressed. "My expectation of course was to get a victory and so, of course, I'm not happy with the result".
"We had 20 shots, but majority were off target, if we had more focus, we could have worked their goalkeeper more", he said. "If we were a bit more concentrated, we could have made the goalkeeper work a little more given the number of attempts we had".
"Firmino is in a very good moment so I trust him", said Tito.
Liverpool's No.9 was introduced 12 minutes from time at the Rostov Arena as Selecao coach Tite sought a late victor after Steven Zuber had equalised Philippe Coutinho's opener. "I'm proud of my lads". Or, should we say, he was rendered ineffective to an extent by some physical play by the Swiss.
Paulinho passed up a glorious chance when his scuffed effort off a cutback from Marcelo from close range was turned behind by Yann Sommer.
The coach of the Selecao was adamant Switzerland's goal should have been ruled out by referee Cesar Ramos, and Neymar agreed with that assessment. But they couldn't get another one in front of a very Brazil-friendly crowd at the Rostov Arena.
Brazil drew Sweden 1-1 back then, the same score of its match against Switzerland in Rostov-on-Don on Sunday, when all the hype surrounding Neymar and his teammates turned into disappointment and concern. Tite's men ended as they had begun with a series of chances for a late victor as Neymar and Roberto Firmino headed straight at Sommer before Miranda dragged a shot inches wide.
And deep into added time Schar's outstretched leg turned a goalbound effort from Silva wide as Switzerland held out for a vital point.
Costa Rica now await on matchday two, before they lock horns with Serbia in their final game of the group stages on June 27 as they continue the chase for their sixth-ever world title.
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