The United States, therefore, is headed back to World Group qualifying for the second time in the last three years.
Blake, who thrashed Mario Ancic on Friday, had to win the fourth match of the competition to keep the U.S. hopes alive, but he slumped to a 6-3, 6-7 (5-7), 6-4, 6-3 defeat in front of a vocal crowd at the Hall Dom Sportova.
In the 103-year history of the Davis Cup, the United States has 60 finals appearances and 32 championships, both records. But it has not captured the title since 1995.
"I think this probably is the most emotionally (difficult) defeat to take," said Blake, who lost for the third time in 10 Davis Cup matches. He was unable to fill the void left by the absence of Andy Roddick and former world No. 1's Pete Sampras and Andre Agassi.
Roddick was injured at last month's Australian Open while Sampras and Agassi have made participating in Davis Cup a lower priority in recent years.
Blake might have been the highest-ranked player in the United State's first meeting with Croatia at No. 24, but Lubicic was the dominant player over the weekend. He won both his singles matches and teamed with Goran Ivanisevic to take the doubles, lifting his country to its second straight World Group quarterfinal.
"This is big for me, especially because I won all three matches," Ljubicic said. "When you are No. 1, your teammates expect you to win at least two matches, maybe three, so it's a lot of pressure. But I didn't feel one bit of nerves yesterday or today."
Croatia is participating in the elite World Group for only the third time in 10 years. It now travels to Spain for a matchup in April.
The 23-year-old Croatian hit 25 aces and broke serve four times in 12 chances, while Blake managed to convert just one break point in six opportunities.
"He really doesn't let you get in rhythm because he doesn't have a second serve," Blake said. "He has two first serves. If he keeps serving like that, or getting better like he says he can, then after the indoor season I think we'll see him in the top 10."
After a split of the first two sets, Blake saved a pair of break points in the second game of the third set. Ljubicic slipped at deuce of that game, appearing to suffer a leg injury, and dropped his next service game -- the first time he had lost his serve all weekend.
But Ljubicic got the break back at love to level the set at 4-4 and later broke again to take the set.
"I think that was the key, because suddenly I won the set without really thinking about it, which is good for me," Ljubicic said. "James is a great player, but I don't think he played as well from the baseline as he did on Friday."
The Croatian gained the crucial break in the sixth game of the fourth set and held on to win, much to the delight of 3,500 faithful.
Ancic defeated American Taylor Dent in the final singles match for a 4-1 triumph.
France also won its tie four matches to one over Romania in Bucharest. After the French clinched the victory with Saturday's doubles, Romania's Victor Hanescu defeated Fabrice Santoro, 6-1, 6-4, and Nicolas Escude of France topped Gabriel Trifu, 7-6 (7-3), 4-6, 6-4.
In the quarterfinals, France will host Switzerland, which edged the Netherlands on the road in Arnhem.
Australia and Spain will square off in the quarterfinals after sweeping their foes this weekend.
Australia, led by world No. 1 Lleyton Hewitt, thrashed an overmatched British team that was without its two best players -- Tim Henman and Greg Rusedski.
Spain cruised past visiting Belgium in Seville. Juan Carlos Ferrero and Carlos Moya won both their singles matches and Alex Corretja and French Open champion Albert Costa clinched the tie with a five-set victory in Saturday's doubles.
In the first reverse singles match, Russian Yevgeny Kafelnikov was a shadow of the player that once held the No. 1 ranking and captured two Grand Slams in a 6-2, 6-3, 7-6 (7-5) setback to Jiri Novak that kept the Czech Republic alive.
Russia will visit Argentina in rematch of last year's semifinals.
2014: The Year in Music [PHOTOS]