Several athletes have come under scrutiny after stolen medical records showed they used banned substances for medical reasons under TUE rules.
Briton Froome, 31, said the system is "open to abuse" and must be addressed "urgently" by cycling's governing body, the UCI, and the World Anti-Doping Agency (Wada).
"I have never had a 'win at all costs' approach in this regard," the Team Sky rider said in a statement.
"I am not looking to push the boundaries of the rules.
"I believe that this is something that athletes need to take responsibility for themselves, until more stringent protocols can be put in place."
Froome and Sir Bradley Wiggins, a former team-mate at Team Sky, were among the athletes whose medical records were made public by hacking group Fancy Bears.
There is no suggestion any of the athletes named have broken anti-doping rules.
Froome, whose TUEs for prednisolone in May 2013 and April 2014 were revealed, said: "There are athletes who not only abide by the rules that are in place, but also those of fair play.
"I take my position in the sport very seriously and I know that I have to not only abide by the rules but also go above and beyond that to set a good example both morally and ethically."
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Wiggins, Britain's most decorated Olympian and the first British winner of the Tour de France in 2012, has been criticised for the timing of his TUEs, shortly before major races in 2011, 2012 and 2013.
He said he took the anti-inflammatory drug triamcinolone for allergies and respiratory issues, telling the BBC on Sunday that he was not trying to gain an "unfair advantage" from being allowed to use an otherwise banned steroid.
Team Sky boss Sir Dave Brailsford on Monday said the team did not "do not cross the line" over performance-enhancing drugs and that he had complete trust in their doctors.
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Tour de France winner Chris Froome says athletes must "take responsibility" and not "push the boundaries of the rules" following criticism of the therapeutic use exemption system.