The star-studded team lost their last five matches - the worst run in their history - and finished fourth in the league.
Queiroz gave no response to Madrid's president Florentino Perez's comments yesterday that the coach's appointment a year ago had been "a mistake".
Perez said there had been "disorder and a lack of authority" in the team.
"I have no other comments to make other than expressing my deepest gratitude to all the supporters and to Real Madrid," said Queiroz.
Queiroz, who was Manchester United's assistant coach for the year before he joined Real, hopes to continued coaching but had no plans yet.
"The future is in God's hands and only He knows," he said.
The former coach today received support from Luis Figo. Real's Portuguese midfielder Luis Figo said Queiroz had taken charge of the team when decisions for the next season had already been made. Figo said: "He did what he could, with professionalism. He put his heart into it and did the best he could.
"He came here with the (Far East) tour already arranged, players left the team and none came to replace them.
"Queiroz worked with a professional attitude and with effort.
"After that, if you win or not is down to circumstances."
