The reigning world and European champions made a shock exit from the competition on Wednesday, losing 2-0 to Chile in Rio de Janeiro to put qualification for the knockout stages out of reach.
That result also brought an end to Australia's hopes after their spirited 3-2 defeat to the Netherlands earlier in the day.
Davidson is keen to go out on a high, but recognises that Ange Postecoglou's men will come up against tough opponents in their final fixture of the tournament.
"Spain is going to be a very hard game," he said. "They will want to restore national pride.
"It is all about hard work and preparation. Ange puts his belief in us and we have had time to grow."
Australia led 2-1 during their loss against the Netherlands, and Davidson paid tribute to the sensational Tim Cahill goal that gave the underdogs an unexpected lead.
"The goal that Tim scored was unbelievable," he added. "Full credit to him; it is much deserved."
