A second-half goal by skipper James Perch did the trick for Forest, who upped the tempo after the break and got their reward in Saturday's clash at The City Ground.
Davies said: "We let ourselves down in the first half by being nervous in our play but we showed a great appetite to win the game in the second half and I thought we deserved the three points.
"It wasn't very good sitting in our dugout in the first half and one or two harsh words were said at half-time. But we got the reaction we wanted from the players.
"They are maturing with every game and they now know how to get 1-0 wins, which is very important.
"By getting the win we've brought a number of other teams into the reckoning at the foot of the table but we've just got to take care of what is in front of us."
By contrast, Coventry have little to play for but manager Chris Coleman was at pains to point out that his side still need a point to be mathematically safe following a run that has seen them win only one match in the last 10.
He admitted: "It was criminal to lose the game with a goal 35 seconds into the second half.
"I told the players at half-time that Forest would come out and be in our faces but one of my players switched off and the ball is in our net. We just didn't defend properly and paid the price for it.
"We were deflated by the goal but we should have been ahead in the first half when we created chances but didn't take any of them.
"But the game summed up our season - some good, some bad - but I don't want to finish the season without putting an end to the run that we are in."
Perch's goal came from a cross by Lewis McGugan that Coventry failed to deal with and loan-signing Dexter Blackstock held the ball up and laid it off to an unmarked Perch, who slid the ball under the body of keeper Keiren Westwood.
It might have all been different for Coventry had Freddy Eastwood not missed an open goal in the 29th minute.
Clinton Morrison squared the ball across the Forest goal and Eastwood, unmarked at the far post, inexplicably bundled his effort wide.
Despite their greater possession in the opening half, Coventry almost conceded an opening goal when Luke Chambers thumped a header against the bar from McGugan's corner.
But Forest improved their territorial share of the game in the second half and Chris Cohen and Blackstock both went close to adding to Perch's decider.