The Briton arrived in Bahrain on Wednesday ahead of Saturday's first race of the season and spoke to Sky Sports while walking from the team hospitality to the garages.
"I'm just pleased that the process is over. I obviously can't comment about it but here, very much the focus now on the grand prix and the season ahead and trying to defend both of our titles," he said.
Asked if it was a regret that the process became public, Horner again declined to comment.
"I'm pleased to be here in Bahrain with the team focused on the season ahead," he replied.
"Within the team, it's never been stronger," he added in response to a final query about unity within the team.
Red Bull won 21 of 22 races last season, the most dominant yet, with Dutch driver Max Verstappen taking his third successive title.
Red Bull's parent company in Austria announced in a statement on Wednesday that the grievance against Horner, by a female employee, had been dismissed after an independent investigation.
Horner, who is married to former Spice Girls singer Geri Halliwell, denied all the allegations against him and continued to lead the team through the process.
Red Bull have said the investigation report will remain confidential.
