With the scoreline locked at 1-1 and penalties seemingly imminent, Sampaoli's men were just a few centimetres away from a famous win at the Estadio Mineirao in Belo Horizonte on Saturday as Mauricio Pinilla rattled the crossbar in the final minute of extra time.
The woodwork then crucially came to Brazil's aid again in the shoot-out as Gonzalo Jara hit the inside of the post with his effort after Neymar had scored to send the host nation into the quarter-finals with a 3-2 win.
For Sampaoli, it was a bitter pill to swallow - although he was also keen to focus on his players' stellar showing.
He said: "It (the defeat) was by fate and by the width of the post. It would have been a deserved victory.
"That causes us pain and takes away the chance of making history. But we played against the candidate to win, at home, and we played as equals.
"The Chilean people have to be grateful to the players who represented their flag."
Sampaoli also hinted that an arduous Group B campaign, in which they were pitted against Spain, Netherlands and Australia, may have taken its toll.
"We played extremely intense games with each opponent that we had," he conceded.
