La Roja were beaten 3-2 on penalties by the host nation in Belo Horizonte following a 1-1 draw after extra-time, but it could so easily have been different if a Mauricio Pinilla's shot hadn’t cannoned off the crossbar in the final minute of extra time.
“That near goal right at the end was really hard for us. We so nearly won, it was harsh,” Sampaoli told a post-match press conference.
“If we had scored then we would have made history forever. It would have been the ‘Mineirazo’.”
But while Chile couldn’t follow in the footsteps of Uruguay's 'Maracanazo' side of 1950 by beating Brazil on their home turf, Sampaoli was still full of praise for his battling outfit.
“I’m very proud of my players. I’m proud for Chile. Everyone was against us in the stadium, but we gave everything, we fought hard. The players have represented our country in a beautiful, wonderful way,” he added.
“Our team nearly won today, but moral victories don't count.”
The 54-year-old admitted that he had tried his best to prepare his team for a penalty shoot-out, but their return of two successful efforts from five attempts was down to the pressure of the moment.
“Penalties are something you always train for but when you are on the field, it's always different, it's more luck than anything else.
"We were able to give Brazil a fright. We have shown we are on a level with these great teams. I think Brazil will feel better and more confident after today.”
The Selecao will meet Colombia in the quarter-finals on Friday, while Chile fly home after falling to a fourth World Cup elimination at the hands of Brazil.