In a lively contest, the Samba Boys prevailed through a brace from Neymar and stoppage time strike from Oscar, after Marcello gave Croatia an early lead via an own goal.
However, Nishimura caused controversy by awarding a dubious penalty to the hosts - given against Lovren for an alleged foul on Fred - which was slotted by Neymar.
The Japanese official also disallowed a goal from Croatia's Ivan Perisic, after harshly ruling Ivica Olic had infringed Brazil goalkeeper Julio Cesar in an aerial challenge.
Lovren did not mix his words when asked about Nishimura's handling of the high-profile fixture.
The defender told L’Equipe: “I’m so sad I want to cry. Everyone has seen it, it’s a scandal for Fifa.
“We talk about respect – the Fifa people spoke to us about it – and what happens? It is better the cup is given immediately to Brazil."
The Southampton man added: “I think we played a good game and had the quality to compete with Brazil but not against 12 men.
“We looked at the pictures in the dressing room and everyone is still asking questions.”