Steven Zuber rose above Miranda to head home five minutes into the second half in Rostov-on-Don, cancelling out Philippe Coutinho's first-half strike, though Brazil wanted a free-kick awarded in their favour.
"We need to play in the same way against Costa Rica, we played well, especially considering it was our first game, but unfortunately we couldn't win".
The Paris Saint-Germain most prized asset in a post-match interview said, "I was hit and it was aching, but it's nothing to worry about".
Their promising start could not last and soon Switzerland were sitting back as Brazil passed the ball crisply around the pitch, nearly finding a breakthrough when Paulinho dragged a shot across the face of goal and wide of the far post with 10 minutes played.
Switzerland head coach Vladimir Petkovic talk to his players during Switzerland's official training on the eve of the group E match between Brazil and Switzerland at the 2018 soccer World Cup in the Rostov Arena in Rostov-on-Don, Russia, Saturday, June 16, 2018.
Indeed, it was the first time since 1978 that the Brazil opening game in the World Cup did not end in a win. The five time champions lost their calm as they failed to extend their lead.
A key to Coutinho's good performances with Brazil has been Barcelona teammate Paulinho, the defensive midfielder who has been responsible for giving the playmaker more freedom to help Neymar and the other forwards.More news: Montreal to co-host 2026 World Cup
Brazil forward Neymar has called on the officials at this summer's World Cup to "do their job" following an incident-filled encounter with Switzerland.
All eyes will be on Neymar as Brazil kick-off their Fifa World Cup 2018 proceedings with a match against a team ranked just four places below them. Two thirds of the match I was happy, then the opposition grew stronger and we were not blocking enough.
With this, Brazil's momentum had dissipated and the tempo of the match apparently slowing down. We should have made their keeper work harder than that.
Brazil thus had to settle for a 1-1 draw in their opening game, with Sommer pulling off a superb save late on to save Switzerland, as they got their campaign off to an underwhelming start, much like fellow favourites Spain, Argentina and Germany. Sometimes if there is a lack of recognition that is a pity because we have played very well.
"I guess it was foul", he told reporters. We showed and demonstrated that this team always believes in itself and can achieve results.
Sunday's other group E clash saw Serbia beat Costa Rica 1-0 thanks to Aleksandar Kolarov's free-kick victor.