A lot of the focus after the game was on whether Brazil defender Joao Miranda had been fouled by Steven Zuber when he headed in Switzerland's 50th minute equaliser, while a decision to deny Gabriel Jesus a penalty was also heavily scrutinised.
Brazil meet Costa Rica on Friday, before finishing their Group E fixtures against Serbia.
Shaqiri is confident of Die Nati's chances of progressing from the group stages after taking a vital point against the five-time world champions.
The Usain Bolt's Tracks and Records crowd went wild with Brazil but numb with Switzerland on Sunday as the Market Place-based restaurant attracted hundreds to watch the World Cup clash between the two nations. Costa Rica, so far, has none.
Brazil joined the list of big teams struggling to win their opening matches at the World Cup in Russian Federation.
"Playing against Brazil and Spain, we demonstrated we could react, that this team always believe in ourselves and can get results".
The Brazilian marking for the goal was woeful, although they will point to a push from Zuber on his marker, Miranda, just before the goal. "I put it down to stress, first match nerves, that's true for me too", the Brazil boss said.
Switzerland concentrated their defensive effort and kept Brazil's unsafe attack under wraps, though the Nati fans held their breaths in the 88th minutes on Neymar's header, which Sommer was able to collect comfortably despite the star having room.
APBrazil joined the list of big teams struggling to win their opening matches at the World Cup in Russian Federation.
Brazil need to improve on dead balls, said Tite. Four years ago, things reached its nadir when the Brazilian star striker was literally kicked out of the tournament during the 2-1 quarterfinal win over Columbia.
A shaky warm-up campaign had called into question the dominant form the Germans showed in qualifying, but experience and records were on their side, having won every opening game at major tournaments since Joachim Loew took over as coach in 2006. "Sometimes if there is a lack of recognition that is a pity because we have played very well".
Brazil would go on to lose 7-1 to Germany in the semi-final without Neymar - one of the most humbling defeats in the competition's history.