Jorge Sampaoli's men impressed in the group stage and are many people's dark horses to go far in the tournament.
After a 3-1 win over Australia in their Group B opener, Chile employed a high-pressing game to great effect when beating Spain 2-0, a result which sent the defending champions crashing out.
A 2-0 reverse to Netherlands followed in Chile's final group match, as the South Americans finished second in the group, setting up a clash with hosts Brazil in Belo Horizonte on Saturday.
Beausejour, who scored against Australia, is of the opinion that Chile's strong showings will see them come up against opposition sides determined to stifle them.
"The better we become the more respect we're getting," he said.
"We've deserved the wins we've had. But now, when things get tough, is the time for us to learn and react.
"We have to learn how to break down a packed defence and deal with teams that play a very cautious game."
Sampaoli concedes that home nation Brazil will be strongly fancied to succeed in front of a partisan crowd, but insists his team will enter the second-round clash with no fear.
"They're everyone's favourites," he said. "I'm proud of this Chile team.
"We're going to play with commitment, courage and our heads held high, ready to face whatever's thrown at us."
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