The Australian fancied his chances of winning the race at the Marina Bay Street Circuit on Sunday as he started P3 on the grid behind Sebastian Vettel in the Ferrari and his Red Bull team-mate Max Verstappen.
Lewis Hamilton has claimed a surprise win at an incident-packed Singapore Grand Prix with Australia's Daniel Ricciardo finishing second for Red Bull and Hamilton's Mercedes teammate Valtteri Bottas third.
Verstappen - who qualified second on the grid - made a good start, but so did Raikkonen from fourth and he was soon alongside the 19-year-old's vehicle.
With Hamilton in control of the race and on course to pick up vital points wherever he finishes, Vettel acknowledged the situation was not what Ferrari had wanted - particularly given their dominance over Mercedes throughout the weekend - but he remains confident of challenging for a fifth drivers' championship. Whatever the cause, the German was out of the race - and his title rival in the lead... Made contact and that was it.
Stewards summoned Vettel, Raikkonen and Verstappen to a meeting after the race but no driver was deemed responsible and no further action was taken.
Alonso, meanwhile, bravely continued but retired on lap 9.
After a few laps behind the safety auto, the race resumed for real on lap 7.
Asked whether Ricciardo could have won if not for the gearbox problem, Horner said: "We certainly could have been closer and put a bit more pressure on".
On lap 11 Daniil Kvyat outbraked himself at Turn 7 and buried his Toro Rosso in the wall beyond the run-off area.
After the incident on the opening lap, Hamilton led throughout and remained uncallenged by Daniel Ricciardo who followed the Mercedes driver around for two hours in second place.
The safety auto came out again shortly after, as Daniil Kvyat crashed his Toro Rosso.
With Hamilton starting fifth, everything looked set for Vettel to retake the overall lead that he had surrendered only two weeks earlier at Monza in Italy. By the time the race re-started again on lap 15, Ricciardo had changed tires, but not Hamilton.
Despite the slight tyre disadvantage, Hamilton again built a lead over Ricciardo at the restart on lap 14.
Ricciardo insisted having to manage the gearbox did not play a major role in the outcome, and he was disappointed that Red Bull's early weekend form did not continue into the race.
The safety vehicle came out again, after Marcus Ericsson's Sauber stalled on lap 39.
Verstappen, who had started from second, blamed Vettel.
The safety auto cuts the leader's momentum and enables others to close the gap. "Hopefully the next races are more in our direction". Romain Grosjean took ninth ahead of Esteban Ocon's Force India in the final points paying position in tenth.