De Gea was at fault for Portugal's second goal as he failed to save Cristiano Ronaldo's speculative shot from the edge of the penalty area in the 44th minute, as the ball found its way into the back of the net.
"The mister [Spain head coach Fernando Hierro] is with me and the whole team. I am calm. It is a mistake that can happen to any goalkeeper. A difficult ball. [We need] to continue training and to do things well in an important game against Iran because we have strong options to win," De Gea told journalists.
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The Manchester United goalkeeper failed to save Ronaldo's speculative shot in the 44th minute with the ball squirming into the goal.
"We are a team. Players have good days and bad days. But we are a family, we are a team… It's all of us together, we are not leaving anybody lying on the wayside… We are cheering the team on… We are not going to point fingers and blame anyone or criticize anyone… Every player is extremely important," Hierro said.
He added that he was proud of his squad and how the team played against Portugal.
"Spanish players are extremely professional. They went on the pitch to give their best. They are very motivated… I hope they will continue to show this strength as we progress," Hierro said.
The 2018 FIFA World Cup kicked off on Thursday and will continue until July 15, with a total of 64 matches set to be played at 12 stadiums across 11 Russian cities.
Spain will face Iran in Kazan on June 20 before taking on Morocco in Kaliningrad on June 25 in their other two Group B matches. Spain head coach Fernando Hierro said he was supporting his team's goalkeeper David de Gea who made a costly error during Spain's 3-3 draw with Portugal with Sochi on Friday.