Davies' men were 9-6 ahead after 25 minutes when Wales international Williams saw red for a tip tackle on opposite scrum-half Benoît Paillaugue.
Williams will now face an ERC disciplinary hearing this week where he will discover whether he will be forced to serve a ban for the tackle.
And Davies, whose side's next RaboDirect PRO12 clash is at home to Scarlets, insists he is desperate to get Williams back on the field as soon as possible.
"It was a bit of a rustic challenge, I think we will contest it but we will have to have a look at it. I am not sure it was the right decision," he told Wales Online.
"It was unfortunate as in the last few weeks Lloyd has been playing really well.
"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."
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