The night also saw Amy Fearn replaced injured referee Tony Bates in the 71st minute.
While Davies believed his side had been dominant, he urged Forest to enjoy the rest of the season as they sit third in the Coca-Cola Championship.
He said: "I think we controlled the game for 30 minutes. They scored against the run of play in terms of possession but saying that we didn't have enough cutting edge chances.
"We sit four points off the top of the league and we are in a wonderful position with 16 games to go.
"We've got to appreciate the position we're in and look forward to the remaining matches. I'm said to the players that this is an experience for them and they should enjoy it.
"They should be proud of where they are. They've given themselves a great chance and there will be no disappointments."
Forest dominated the first quarter of the game starving Coventry of any worthwhile possession without creating enough clear-cut chances.
Joe Garner forced Keiren Westwood into a sixth-minute save but most of Forest's work was happening in areas which did not cause the home side any real problems.
Davies' men were made to pay in the 25th minute when Clinton Morrison produced some clever work down the left flank and crossed the ball into the box. Richard Wood piled in and when his shot was saved by Lee Camp, Eastwood finished off from close range.
Forest came storming out the blocks and Radoslaw Majewski looked the most likely to pull the visitors back into the game when he shot just over in the 60th minute.
The away side, however, failed to maintain their grip on the game, and Coventry came back strongly in the second half.
Eastwood could have added a second in the 65th minute before Gary Deegan failed to finish a flowing move when he fired wide of goal after great work from fellow sub Carl Baker.
The game was then held up when referee Bates went down with a calf strain and Ms Fearn took over in the middle park to see out the game without controversy, despite six minutes of injury time.
Coventry boss Chris Coleman said: "Forest are one of the best teams in the league so it's a good result. They are strong in every area and we knew it would be a hard match but we have been hard to beat recently and the lads were fantastic.
"Some of our defending was top notch and our strikers did well against a very strong defence.
"We have had a grittiness about us in the last four or five games and that's pleasing.
"We said don't sit back and we didn't - but they pushed us back. We had one or two scary moments but we did well."