"It did not sit well morally with me."
Cycling's use of TUEs, where banned drugs are allowed to be used to treat medical conditions, came under scrutiny, after Russian hackers published confidential details of athletes' TUEs.
Froome's two TUEs were both for a week's oral course of the anti-inflammatory drug prednisolone to treat chest infections that aggravated his asthma in 2013 and 2014.
Former Team Sky team-mate Sir Bradley Wiggins, who also suffers from asthma and became Britain's first Tour de France winner in 2012, was found to have had three TUEs for anti-inflammatory drug triamcinolone, taken on the eve of the 2011 and 2012 Tours de France and 2013 Giro d'Italia.
There was no suggestion that Froome, Wiggins nor Team Sky had broken any rules.
In the past, Froome has spoken about his belief that the TUE system in cycling is open to abuse and he re-iterated his desire for the World Anti-Doping Agency to clamp down on their use.
"The fact that we're having that debate about authenticity means there's a problem with the system," he said.
"I think WADA need to tighten their regulations around TUEs, so they're not something that we question their legitimacy.
"It's not good for sport in general. The fact that we're discussing the validity of results, that brings it back to the authorities.
"It is something they need to tighten up on, so that there aren't questions being asked anymore."