Horner was subject to a detailed probe by Red Bull's energy drinks company over allegations made against him by a female employee.
After a process that took eight weeks, and involved an independent barrister, the complaint against Horner was dismissed on Wednesday, and he was cleared of any wrongdoing.
But with Red Bull having offered almost no explanation for its findings, and making clear it will keep details of the matter private, there has been concern about things having been swept under the carpet.
Speaking at the F1 season opener in Bahrain, Mercedes boss Toto Wolff and McLaren CEO Zak Brown both called on F1's commercial rights holder and the FIA to take steps to ensure everything had been conducted properly.
Asked about Red Bull's findings from the investigation, Wolff said: "Well, I just read the statement, which was pretty basic.
"My personal opinion is we can't really look behind the curtain. At the end of the day there is a lady in an organisation that has spoken to HR and said there is an issue and it was investigated. And yesterday, the sport has received the message: 'It's all fine. We've looked at it.'
"I believe that with the aspiration as a global sport on such critical topics, it needs more transparency. And I wonder what the sport's position is?
"We are competitors. We are a team, and we can have our own personal opinions or not. But it's more like a general reaction or action that we as a sport need to assess what is right in that situation and what is wrong?"
Brown added: "I've read this statement. I think, from what I've seen, there continues to be a lot of rumours, speculation, and questions.
"I think the sanctioning body has a responsibility and authority to our sport, to our fans, and I think to all of us in Formula 1… I think they need to make sure that things have been fully transparent with them."
He added: "I think until then, there will continue to be speculation because there are a lot of unanswered questions about the whole process. I think what's needed by those that run the sport is to really be able to draw a line under it.
"Until then, I think there will continue to be some level of speculation by people, and I don't think that's healthy for the sport."
Wolff felt that simply accepting Red Bull's statement without any extra due diligence taking place regarding the details of the matter would not sit well for F1.
"I just simply think that, as a sport, we cannot afford to leave things in the vague and in the opaque on critical topics like this, because this is going to catch us out," he declared.
