The injury-ravaged Blues were leading 9-6 after 25 minutes of a scrappy encounter when Wales international Williams was dismissed for a tip tackle on opposite number Benoit Paillaugue after the ball had squirted out of a Cardiff scrum.
"It was a bit of a rustic challenge, I think we will contest it but we will have to have a look at it," Davies said. "I am not sure it was the right decision."
The home crowd howled their derision at referee John Lacey, but the official appeared to have been left with little choice after Williams lifted Paillaugue before swinging him around and landing him on the back of his neck.
Williams will now face an ERC disciplinary hearing this week where he will discover whether he will serve a ban for his tackle.
The low end entry point for a dangerous tackle is two weeks, with the high end being a suspension of 10 weeks or more.
Davies added: "It was unfortunate, in the last few weeks Lloyd has been playing really well, but aside from that I thought the way we adjusted and played after that, considering the age of some of the players out there, and the way we played to come back into the game was really pleasing.
"A couple of loose kicks cost us and we did not go through the phases down in their half often enough to get extra penalties or even potentially score a try, but overall the effort and determination was fantastic."
Montpellier coach Fabien Galthie, however, was in no doubt referee Lacey had made the correct decision after seeing his side win away from home for the first time in the competition.
He said: "The law is the law. The player knows the law and he has to respect it. It would have been the same for us. It is a dangerous tackle that deserved a red card."