That approach backfired as Vladimir Petkovic's side slowly took control of the proceedings.
Gabriel Jesus also appealed for a penalty when he clashed with Manuel Akanji in the box, but Marcelo did not want to make excuses for Brazil's inability to turn a dominant display into three points.
Brazil opened scoring on 20 minutes from Philippe Coutinho's long range strike that beat the Swiss' goalkeeper.
Paulinho in particular struggled to replicate the kind of form that had helped him re-ignite his career with FC Barcelona in La Liga this year and he was eventually withdrawn in the second half after fading off as the game progressed.
Brazil's next game is on Friday against Costa Rica, who lost 1-0 to Serbia in their opener.
The Swiss were fortunate to earn a draw when you consider that Brazil had won 37 of the 40 previous World Cup games during which they scored first.
But while he wasn't in peak form, Neymar seemed absolutely desperate to prove that he was.
When he had a late header saved, it looked like there were tears in his eyes as his final chance to show definitively that he was back disappeared.
Despite Brazil's optimism, the team is wary of Sunday's opponents.
The great and the cruel thing about global football tournaments is their randomness, how single moments can decide games and games can decide campaigns. Though they had to go through the play-offs to qualify, Switzerland put together an excellent campaign in the European preliminaries and know what it takes to impress against a big-name team in an opening match, having beaten eventual champions Spain in their first outing at South Africa 2010.
"My expectation of course was to get a victory and so, of course, I'm not happy with the result".
They made a far bigger effort than the Swiss to find a second goal and were not far from finding it. We didn't deserve to end with a draw.
Nick Miller is a writer for ESPN FC, covering Premier League and European football.