The visitors, who had a man sent off, went down 31-25 to their local rivals at the Recreation Ground to suffer their fourth league loss in six matches.
"I was delighted with that last period, the last 30 [minutes] we played with 14 men," Davies told Sky Sports News.
"For the boys to respond like they did was fabulous. That's the character that this team has shown this year."
Fourth-placed Gloucester could find themselves out of the playoff places on Saturday if Northampton Saints beat London Irish.