Despite a late onslaught from the Tigers, Gloucester held on for a 27-21 win to stretch their unbeaten run to six games.
Davies said: "I am really delighted with the overall performance today. We showed great determination in the second half, but we also played some great rugby at times.
"When we were down to 13 players the momentum of the game swung and it was always going to be difficult, but the determination and effort the boys showed was unbelievable.
"We have a lot of confidence and belief and that was a fabulous win for us on what was a fabulous Kingsholm occasion."
Davies has been in his role at the Kingsholm Stadium since June.