There were claims before the clash that the teams would play out a 2-2 draw, which would have sent both through to the next round and left Italy out of the tournament.
But Navas stated that the idea had never crossed the mind of any of the players due to their hunger for glory.
"We, the players, want to to win everything, we always want the victory," Navas told Telecinco. "We look for that because of what we've achieved, and what we want to win [in the future]."
Vicente del Bosque's team faced a stubborn Vatreni rearguard and were unable to find a breakthrough for long periods of the match, before Navas popped up to score late on.
"It was a tough game," he continued. "Croatia had plenty to play for in this match and they played defensively."
Having topped Group C, Spain will now face the runners-up of Group D in the quarter-finals of the tournament.