The loss was the first time the reigning world and European champions had lost a competitive match in just under three years, with their last setback coming at the hands of Switzerland in the opening game of the 2010 World Cup.
"Brazil were better than us and we have to congratulate them," Del Bosque said on Spanish television channel Telecinco.
The Spain boss also thought Fred's opening goal for Brazil, which came just two minutes into the game, set the tone for the evening and admitted the two other goals, scored by Neymar and Fred either side of half-time, arrived at the worst possible time for his team.
"We had some bad luck at the start of the game, at the end of the first half and at the start of the second, but I don't want to make any excuses because they were the better team," he said. "They had more energy than us and they channelled that into every move they made."
Sergio Ramos, who missed an opportunity to get Spain back into the game when his second-half penalty went wide of the target, felt nothing went in his side's favour on the night.
"There are some days when nothing goes right for you and it was like that from the very first minute," he said. "They scored very early on and then they sat back. There was then a lot of space between attack and defence. You have to congratulate Brazil because they knew exactly how to play against us."
Brazil boss Luis Felipe Scolari singled out the support of the fans inside the Maracana, but Ramos added: "I don't think it influenced the game, although it was an advantage for them. For me, it was an extra motivation."
Spain captain Iker Casillas, meanwhile, reflected that the defeat could benefit his team in the long term.
"It will serve as a reminder of what we'll be up against in next year's World Cup," the goalkeeper said.
- Sports & Recreation
- Del Bosque
- 2010 World Cup
- Sergio Ramos