The Light Blues under former boss Giovanni van Bronckhorst were thrashed 4-0 when the two sides met at Parkhead in September.
Beale, former assistant coach under Steven Gerrard, had won his first four cinch Premiership matches since taking over from the Dutchman in November but he had some early thinking to do in his first Old Firm game as boss when Japan striker Daizen Maeda opened the scoring for the visitors in the fifth minute following some lamentable defending by Rangers.
However, the Govan men fought back with a Ryan Kent strike and a James Tavernier penalty but, in the 87th minute, Japanese forward Kyogo Furuhashi flashed in a shot from 12 yards to maintain Celtic's nine-point lead over the Light Blues in the title race.
Davies said: "I think since the manager has come in he's made it clear we're going in one direction and that's forward.
"We're not going to stand off anyone and we're going to show who Rangers are.
"He wants to take us back to some of the performances the boys put in when he was at the club before. That's what we're trying to do going forward."
The 27-year-old centre-back has recently returned from injury and promised even better performances in the future.
He said: "I'll take more positives from this game than from the past couple of games.
"I kind of struggled to get my fitness right. It takes a few games anyway but hopefully I can stay fit and help the team.
"The more I'm in the team and playing, the better I'll be."
By and large, the former Preston player enjoyed his debut in the Glasgow derby.
"I thought the atmosphere was incredible," he said. "It felt different to a league game or even a European game in my experience.
"The noise when we scored was something I've not heard before.
"I would have enjoyed the experience more if we'd have won the game but I thought it was special."