Spain were dumped out in the group stage at the finals in Brazil after embarrassing defeats by Netherlands and Chile.
A surprise loss to Slovakia in Euro qualification Group C also set back their bid for a place at the tournament in France in 18 months time.
They also slipped to friendly defeats by France and world champions Germany as La Roja came crashing back to earth after six years of dominating the global game.
"We had a necessary period of reflection after the World Cup and both we and the federation remain on the same page," Del Bosque said on the national team's website (www.sefutbol.com) on Tuesday.
"We decided to carry on and I am feeling in good spirits and full of desire to fulfil my responsibilities," added the 64-year-old, who came close to quitting after the World Cup before the Spanish soccer federation (RFEF) persuaded him to stay on.
"We are not a burden for the national team but we are trying to create a new side to compete in the way we were before," Del Bosque said.
"Our objective is clear: qualifying for the European Championship in 2016."
With four matches played in Group C, Spain are second on nine points behind Slovakia, who have won all four of their games.
Ukraine, who Spain host in Seville on March 27, also have nine points in third, with Macedonia on three and Belarus and Luxembourg on a point each.
After hosting Ukraine, Spain play the Netherlands in a friendly in Amsterdam on March 31 and the showdown with Slovakia is in Spain at the beginning of September.
(Reporting by Iain Rogers, editing by Ed Osmond)
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