Murray, who reached the Australian Open final at the beginning of the month, had 55 unforced errors and only 15 winners against the Croatian teen. Many of his shots were landing in the net or sailing beyond the lines.
"I would definitely say I was a little bit sluggish at the beginning of the match, but in the second set I definitely started to move a bit better and play a little bit better," Murray said. "But, yeah, I started the match not good."
Coric, who never offered Murray a break-point opportunity, reached his second career ATP level semifinal. His first was last year in Basel, Switzerland, after beating Rafael Nadal.
"He didn't make many errors," said Murray, who won his only other match against Coric in 2013 in the Davis Cup. "He played very solid and he moved well.
"I made way too many mistakes from the beginning of the match right through to the end."
The 84th-ranked Coric briefly wobbled when he was at 2-1 in the second set.
"I lost my focus I think somewhere in the second set on 2-1," Coric said. "Actually, I started to realize that I can win this match, so I started a little bit (to) overthink.
"But after two games I think I got back at my focus."
Coric will next face wither defending champion Roger Federer or Richard Gasquet.
Coric entered the main draw as a lucky loser after Philipp Kohlschreiber withdrew. And on Wednesday, he was tied at 4-4 in a third set tiebreaker when Marcos Baghdatis retired from the match with cramps.
"I know I got a little bit lucky with coming in the main draw," Coric said. "And also yesterday, I think I was actually very lucky because I was 4-1 down, double break, and also 5-3.
"But that's tennis and that's life and another day."
Also, fourth-seeded Tomas Berdych advanced by beating Sergiy Stakhovsky 6-3, 4-6, 6-2. He will next face either Novak Djokovic or qualifier Marsel Ilhan.