The reigning world and European champions were stunned as Robin van Persie and Arjen Robben netted twice each in the Group B clash on Friday.
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"I feel bad, I’m disappointed, but [we] have enough courage to get over the defeat. We came out well and then the first half ended in a draw," he told TVE.
"The dressing room has responded well because we’re a squad of professionals and good guys, both those who’ve played and those that didn’t. There are no accusatory glares.
"There was an uplifting conversation and it’s good for the team. We have to talk about it."
Xabi Alonso had given Spain a 27th-minute lead from the penalty spot before the Dutch dominated the second half after Van Persie's stunning diving header just before half-time.
Robben netted twice after the break alongside efforts from Van Persie and Stefan de Vrij as the Netherlands cruised to victory in the 2010 World Cup final rematch.
Del Bosque, who refused to blame goalkeeper Iker Casillas for the loss, said his team would need to improve their defence.
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"Today we were very loose and we’ll have to put something in place that we should’ve had for Van Persie and Robben.
"In the first half we found space. We found avenues with (Andres) Iniesta and (David) Silva ... everything seemed to be going well until we were on our back heels.
"They left us depressed while they were in a state of euphoria."