A 93rd-minute own goal by the unfortunate keeper Yann Sommer from a Bryan Ruiz penalty gave the central American side a deserved 2-2 draw.
It's not the first time Capello has singled out Paris Saint-Germain striker Neymar for criticism, saying in 2014 that he had "a very annoying attitude" and "falls to the ground every time you touch him".
Switzerland would like to post a win and ensure that there are no glitches on their way to the Round of 16.
Switzerland would be hoping to seal off a Round of 16 spot from Group E.
Neymar received the support of his Brazil teammate Fagner after his tears at the end of their World Cup win over Costa Rica and subsequent criticism at home.
Neymar limped out of a training session with a sore right ankle following Brazil's opening 1-1 draw with Switzerland last weekend.
A largely frustrating afternoon for the five-time world champions was forgotten thanks to two goals in stoppage time.
At the final whistle, Neymar sat down on the grass and wept, with the emotion of victory hitting home after the tense Group E contest at the Saint Petersburg Stadium.
FIFA World Cup 2018, Highlights Brazil vs Costa Rica: Neymar, Coutinho on target as Brazil break stubborn Costa Rican defence.
Neymar will play in Brazil's vital World Cup match against Costa Rica despite injury fears, coach Tite confirmed.
Should Neymar not be fit, Coutinho could be moved into his role on the left of a front three with Tite bolstering his midfield.
Even before his latest setback, there were doubts over Neymar's fitness heading into the World Cup after a three-month layoff.
Neymar was back in training for Brazil 24 hours after limping out of a session with an ankle problem.
World Cup 2018, Costa Rica vs Serbia: This win puts Serbia in a strong early position in Group E ahead of games against Brazil and Switzerland
FIFA World Cup 2018, Highlights Costa Rica vs Serbia: Roma defender Aleksandar Kolarov's wonder goal helped Serbia beat Costa Rica 1-0 in a Group E match.
Oscar Ramirez-coached Costa Rica, the aim in this World Cup is to improve on their best performance of a quarter-final.
The Real Madrid goalkeeper Keylor Navas was a key player in Costa Rica's quarterfinal finish in 2014.
Hazard was forced off in the 70th minute after an apparent knock to his right ankle as Belgium sparkled against their fellow finalists with a powerful brace from Romelu Lukaku.