The investigation into the punctured tyre that ended the world champion's race on Sunday after only one corner was completed at Yas Marina Circuit yesterday.
Pirelli, the Italian manufacturers, said their tyre was not to blame and added that there was no evidence of debris, as previously suggested by Horner.
"We can confirm that a structural failure was not the cause of Sebastian Vettel's deflation in Abu Dhabi, a conclusion that we have arrived at together with Red Bull Racing following a detailed examination and analysis of the remains of the tyre," Paul Hembery, the motorsports director for Pirelli, said in a statement.
"We cannot rule out debris on the track causing damage to the tyre, which then provoked a deflation, but having looked at the track closely there is no direct evidence of this."
Horner, in an interview with Autosport, confirmed his team had worked alongside Pirelli during the examination of the tyre's remains, but added the case remained unsolved.
"We have worked hard with the full assistance of Pirelli to find an answer, but unfortunately when you are presented with a bag of bits it is almost impossible to come up with a firm answer," Horner said.
"There is nothing on the data to suggest there was anything wrong with the tyre before the start, but when he ran across the kerb on the exit of Turn 1 there was an instant deflation. We believe the most likely cause of this was a foreign object penetrating the tyre, but we may never find the true answer."
Horner refused to entertain the possibility that the tyre's inner sidewall had become overheated from exhaust gasses being blown on it and said footage that showed smoke emerging from Vettel's rear tyre was burning bodywork and not burning rubber.
"There was some worn bodywork that got burnt, and that gave the appearance of smoke from the tyre after the start," he said. "Sebastian's start procedure was … the same it had been all season. We were also running in the same configuration as before, so there is no reason why we should suddenly suffer a problem."