Ricciardo was sitting in fourth on the ninth lap of the race when his vehicle conked out on him - his fifth DNF in 10 races.
Despite a strong start, Ricciardo's race came to a rude end when his RB14 lost all power halfway through the hairpin at Turn 11.
Although reliability for the team's factory cars has been fine, it is believed Renault has now slipped behind the most recent upgrade of Honda - the team set to supply Red Bull next year.
Ricciardo, who now races for Red Bull alongside Max Verstappen, was forced to retire at the US Grand Prix on his ninth lap due to a mechanical failure.
Max Verstappen carved his way from 18 on the grid to finish second, while Lewis Hamilton finished third.
"It was a crying shame for Daniel and I feel so sorry for him", Horner told Sky.
"For Daniel, having started the race strongly and looking so competitive it was hugely frustrating to lose him so early on with what looks like a repeat issue of Bahrain, where the engine energy store is suspected to have failed terminally", said Horner.
"He's just taken his frustration out on his room by putting his fist through the wall, which you can totally relate to".
The Aussie failed to finish a race for the seventh time this season - more than any other driver - after a power unit issue ended his US Grand Prix after just 10 laps.
It continued Ricciardo's tough spell and means he has still not been back on the podium since winning May's Monaco Grand Prix. The Renault guys in the garage have obviously apologized, which we appreciate it, but the frustration is for Daniel.
"He doesn't blame the [Red Bull] team in any way, he knows we are doing everything we can, it's just one of those things".
Vettel's hopes of a victory to reboot his title bid were wrecked when he clashed with Ricciardo's Red Bull on the opening lap.
"I think within the team there are secretly some jokes being made about it".