Brazil showed a resilient streak not normally associated with the Samba Stars, playing 33 minutes with a man less following Ronaldinho`s controversial dismissal.
Brazil held firm to preserve their 2-1 lead and see off England.
Scolari implied that his decision to play with ten in training had raised eyebrows, but feels it was now justified.
"We train many times with ten players and the Brazilian press does not understand this," commented Scolari.
Scolari had nothing but praise for his side following their successful quarter final win.
He added: "I have a deep admiration for this team.
"The spirit within this camp is superb, this was one of the reasons why they were able to secure their place in the semi-finals of the World Cup.
"All the players deserve great credit. It is a job well done and gives me a sense of great personal satisfaction.
"I have never seen the team defend the national colours with such fighting spirit. We are doing well."
Scolari feels Ronaldinho`s dismissal was harsh, adding: "Ronaldinho was fouled by an England player just before it. He didn't intend to foul anyone."
Brazil captain Cafu was pleased with the performance but feels nothing has been achieved yet.
He said: "It is good to be in the last four, but we have not yet achieved anything.
"We have to keep working, we will still have a hard match in the semi-finals."
Cafu issued a comment for the critics, adding: "This victory is for the people who did not believe in us.
"Now we need to see if they will believe in us."