Del Bosque said the bureaucratic hang-up was his fault for not having called up Diego Costa earlier.
The former Real Madrid manager said he had spoken to Diego Costa personally and they both shared the desire that he play for Spain.
Del Bosque said in private Diego Costa sheds his sometimes abrasive on-pitch attitude.
“We had a pleasant conversation with a very nice, polite young man who is completely different from the aggressive Diego Costa we see in games,” he said. “We were all very comfortable in the meeting. There was no commitment, but he would like to come.”
However, Del Bosque was careful to stress that “until he plays for the team he is still free to choose” and could end up playing for Brazil.
The Spanish football federation said in a statement on Thursday that world football's governing body had asked it to provide documentation certifying that Diego Costa had not played for Brazil before. The Spanish federation said it had in turn asked the Brazilian federation for said proof.
Xabi Alonso, Carles Puyol, Jordi Alba, and Santi Cazorla were also left off as they recover from injury.
Del Bosque called up 21-year-old Sevilla defender Alberto Moreno for the first time to fill in for Alba at left back.
Spain:
Goalkeepers: Iker Casillas (Real Madrid), Victor Valdes (Barcelona), Pepe Reina (Napoli)
Defenders: Alvaro Arbeloa (Real Madrid), Juanfran Torres (Atletico Madrid), Gerard Pique (Barcelona), Raul Albiol (Napoli), Sergio Ramos (Real Madrid), Ignacio Monreal (Arsenal), Alberto Moreno (Sevilla)
Midfielders: Sergio Busquets (Barcelona), Mario Suarez (Atletico Madrid), Xavi Hernandez (Barcelona), Andres Iniesta (Barcelona), Jorge “Koke” Resurreccion (Atletico Madrid), Francisco “Isco” Alarcon (Real Madrid), Cesc Fabregas (Barcelona)
Forwards: Pedro Rodriguez (Barcelona), Jesus Navas (Manchester City), Juan Mata (Chelsea), David Silva (Manchester City), David Villa (Atletico Madrid), Alvaro Negredo (Manchester City)