Scolari's men managed to hold on to their lead to reach the last four of the tournament, where they will take on Germany.
Scolari told reporters: "We didn't have a problem with tiredness after the Chile game and the team made a full recovery, as you could see in the first half.
"If we'd have got the second goal then, it would have settled our nerves a bit more. The goal we conceded came about because we gave away possession and were caught off balance.
"They really committed men forward, with three strikers and James dropping into space. Our front men had to do a lot more running too, but we got there in the end. We've still got two steps to go but we've got the ability to get there."