"I gave him too much, I guess," Hayward said after the 87-84 defeat.
The first meeting between Hornacek, an assistant with the Jazz from 2011-13, and his old team was an ugly one.
The Suns lacked energy, giving up 22 offensive rebounds. The Jazz, meanwhile, turned the ball over more than 20 times and missed 10 free throws for a second straight game, resulting in another 3-point defeat.
"Mistakes cost you games, especially on the road," Jazz coach Ty Corbin said.
Before the game, Hornacek joked he might confuse the game with a practice.
Many times as the Utah Jazz scrimmaged over the last three years, it had been his job to coach the team's youngsters. Friday night, he watched his former pupils Hayward, Derrick Favors, Enes Kanter and Alec Burks get the Jazz to the brink of victory before coming up just short.
"These guys are all great players, and to watch them go from their rookie years to where they're at now, except for when we play them, it's exciting to watch," Hornacek said.
For the second time in as many games, the Jazz took the game down to the wire.
After watching his buzzer-beating effort rim out on opening night, Hayward hit a 3-pointer to tie things up with 16 seconds left.
Bledsoe, however, would play spoiler.
The point guard scored Phoenix's final 14 points of the game and finished with a team-high 18.
While Hornacek's Suns improved to 2-0, the Jazz lost another close game. Still, the new head coach said he sees promise in the team he once helped mold.
Hornacek called Jazz big men Derrick Favors and Enes Kanters "monsters on the boards" and the two post players lived up to the billing, grabbing a combined 29 rebounds on the night. In all, the Jazz out-rebounded Phoenix 53-46.
Kanter, Favors and Hayward each finished with a double-double in the loss.
A day after his contract extension talks with the team fell apart, Hayward scored 18 points and grabbed 10 rebounds. He hit one game-tying triple late, but stepped out of bounds trying for another with less than a second left in the game.
Hornacek spoke highly of Hayward before the game. He compared Hayward's development with his own, adding that he believes the Jazz swingman is a year ahead of where Hornacek was at the same point in his career.
"I truly believe in a couple years he could be an All-Star in this league," Hornacek said.
Burks continued to play the role of sixth man, coming off the bench to score 15 points. But the rest of the Jazz reserves chipped in just five points in the loss.
The Jazz's offense as a whole left Hayward, the team's young leader, wanting.
"We've got to be able to execute down the stretch," he said. "Too many turnovers, too many, not necessarily bad shots, but they weren't good shots."
For a young Jazz team that will likely see its share of struggles on the road, Friday's loss was a squandered opportunity. Utah now returns home to face the Rockets, before leaving on a difficult four-game East Coast road trip next week.
"It's tough, especially losing by three points," Favors said. "But you've got to have a short memory and get back to it tomorrow night."
O Eric Bledsoe scores the Suns' final 14 points, including a game-winning 3-pointer.
• The Jazz commit 21 turnovers and make only 17 of 27 free-throw attempts.
MORE COVERAGE • Gordon Hayward says he has no hard feelings toward the Jazz about not reaching contract extension Thursday night. > D4
Rockets at Jazz
O Saturday, 7 p.m.
TV • ROOT
About the Jazz • Fourth-year swingman Gordon Hayward and the Jazz couldn't agree to an extension before Thursday's deadline, but Hayward is still the team's leader.
About the Rockets • The summer's biggest acquisition, Dwight Howard, seems to be back in form; he grabbed 26 rebounds in his Houston debut.
• See Scoreboard for Friday night's box score > D7