Gloucester's 27-21 victory - their sixth successive league game without defeat - owed much to a 17-point haul from fly-half Freddie Burns and wing James Simpson-Daniel's brilliant attacking invention.
But they also memorably kept Leicester at bay for almost 10 minutes in the second half when they were down to 13 players after scrum-half Jimmy Cowan and full-back Rob Cook had been yellow carded.
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."
Leicester rugby director Richard Cockerill saw the Tigers leave Gloucester with only a losing bonus point despite his forwards dominating much of the action.
"It was a great game of rugby," Cockerill said. "We got ourselves back into it and put them under huge pressure, but I don't know how many times you have to get penalised two metres from your line before people go to the sin-bin, which was frustrating.
"If you were killing a ruck three times on the trot you would be in the bin; if it was a scrum you would be in the bin. There were some pretty tough calls.
"But look, we made mistakes ourselves at times and it was a classic game of rugby. Fair play to Gloucester, they played some good stuff."
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