The Roja boss was pleased with the victory against Bilic's strong side, adding that the pre-match speculation over the 2-2 draw prediction was a hindrance
Spain coach Vicente del Bosque was visibly relieved after this side's hard-fought 1-0 victory over Croatia in Gdansk.
A late goal from substitute Jesus Navas was enough for La Roja to progress to the quarter-finals ahead of second-placed Italy, and send Slaven Bilic's men out of the tournament.
The veteran manager praised his team's performance against a stubborn Croatia side, and praised the impact of two second-half substitutes in helping them to victory.
"It was a very tough match," Del Bosque told Telecinco. "They [Croatia] played well defensively and gave us no space.
"Cesc Frabregas got into the game to gave us some fresh oxygen, and Navas provided more for us in attack."
The World Cup-winning boss also dismissed any pre-match speculation regarding the possible 2-2 draw that would have sent Italy out.
"We've take off our back all of this mess about the draw. It was more a weight to deal with than an advantage," the 61-year-old added.
"The result would have been good for us, but maybe this [draw prediction] made us a bit confused."
Spain will now have to wait until the culmination of Group D on Tuesday night to find out who their quarter-final opponents will be.