Horner was in the Bahrain paddock on Thursday morning after he was cleared of “inappropriate behaviour” towards a female colleague.
Speaking on Sky Sports ahead of the opening round of the Formula One season, Horner, 50, said: “I am pleased that the process is over, and I cannot comment about it.
“I am here to focus on the grand prix and the season ahead and trying to defend both of our titles.”
Horner added: “I can’t give you any further comment, but the process has been conducted and concluded.
“I am pleased to be here in Bahrain, and with the team, focused on the season ahead. Within the team it (the unity) has never been stronger.”
Red Bull Racing’s parent company Red Bull GmbH announced on February 5 that Horner was under investigation following an accusation made against him by a female colleague.
Horner emphatically denied the claim and, on Wednesday, he was cleared of wrongdoing.
Red Bull GmbH said it was confident the investigation had been “fair, rigorous and impartial”, but added that the report – understood to stretch to 150 pages – is “confidential”.
Mercedes boss Toto Wolff had called for the investigation to be conducted with transparency but no details of the allegations against Horner were reported. The complainant also has a right to appeal against the verdict.
Addressing the controversy on Thursday, Williams team principal James Vowles said he has to believe Red Bull’s process has been thorough.
Vowles said: “I have a responsibility for Williams, and if anything like that happens here, I would want to make sure we properly investigate it and do a robust process that is clear to the outside world what has happened and what we can do to rectify that.
“I trust that Red Bull have done a strong process and we have to in that circumstance.
“But what I want is us as a sport to be proud that we are sitting on a set of foundations that is one of inclusivity, one of openness and transparency and all I ask in that matter is that we make sure we have faith and trust that all of the organisations are working for the same standards.”
A statement from Red Bull GmbH on Wednesday read: “The independent investigation into the allegations made against Mr Horner is complete and Red Bull can confirm that the grievance has been dismissed.
“The complainant has a right of appeal. Red Bull is confident that the investigation has been fair, rigorous and impartial.
“The investigation report is confidential and contains the private information of the parties and third parties who assisted in the investigation, and therefore we will not be commenting further out of respect for all concerned. Red Bull will continue striving to meet the highest workplace standards.”
Horner, who has protested his innocence throughout, was questioned by a lawyer for eight hours earlier this month at a secret London location.
Horner has been Red Bull team principal since they entered F1 19 years ago and is the longest-serving boss on the grid.
He has overseen seven drivers’ world championships and six constructors’ titles.
Red Bull have dominated the sport in recent seasons and last year won 21 of the 22 races with Dutch driver Max Verstappen setting a new record for 10 consecutive victories as he wrapped up his third title.
Horner, who is married to former Spice Girls singer Geri Halliwell, was awarded a CBE for his services to motorsport in the New Year Honours.