Brazil took the lead through what appeared to be a Gonzalo Jara own goal in the 18th minute of Saturday's game, but Chile struck back just after the half-hour mark through Alexis Sanchez and were the better team for much of the second half of normal time.
Mauricio Pinilla went within inches of earning them a famous victory in the closing minutes of extra-time when his shot rattled the crossbar, but the substitute was ultimately one of three Chile players to miss from 12 yards in the resulting penalty shoot-out as Brazil won 4-3 on spot-kicks, the game having ended 1-1 after extra-time.
Sanchez and Jara were the other guilty parties, but Sampaoli had nothing but praise for his players after the game.
He said: "We wanted to win the game before going to penalties. I don't know if Brazil will win this World Cup.
"I don't believe in moral victories. They don't count. We were on par with these teams. Football is like this.
"I told them to fight, be brave and defy history. Looking ahead, we have to keep going on that path.
"We had players who risked their health for the national team. I can't ask more of them and am proud of our team."
Midfielder Arturo Vidal added: "We played well, but had no luck. The ball did not bounce in off the crossbar. We left our souls on the field."
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