Argentina had their chances in Belo Horizonte, but fell after goals from Gabriel Jesus and Roberto Firmino for Brazil.
Sergio Aguero and Lionel Messi hit the woodwork for Scaloni's side, who enjoyed plenty of possession after the hosts opted to sit back having gone 1-0 up.
Scaloni, who was unhappy with the refereeing amid suggestions Argentina could have been awarded two penalties, felt his team deserved a place in the final.
"On merit, the team that should have gone to the final was Argentina," Scaloni told a news conference post-match.
"We were superior to Brazil. We showed that this group of players feel the shirt like nobody [else].
"We leave an image for the future of this national team and a very good way forward."
Aguero hit the crossbar after Jesus' opener, while Messi struck the post in the second half, before Firmino's sealer.
Asked about his future at the helm, Scaloni – in his first management job – said it was not the time to discuss his position.
"I don't think it's time to talk about it, because that's the least of my worries right now," he said.
"I want to be with my players and share this hard moment."
Messi, wearing the captain's armband for Argentina, agreed with his coach's assessment of the match and made a point of questioning the referee's performance.
"They were not better than us. They found the net early and the second goal came from a penalty [to Aguero] they didn't award," Messi told reporters.
"They [the officials] had booked a lot of bullsh*t, but they didn't even check the VAR, that's incredible.
"That happened all over the game. At the first glance of contact, they ruled in their [Brazil's] favour and this kind of bullsh*t distracted us from the game.
"There is no excuses for us, but we need to review this, analyse it and let's hope CONMEBOL does something about it.
"I think we played a great game. We made a great effort and they were not superior to us."