Forest found themselves a goal and a man down midway through the first half after Tommy Smith fired Rangers ahead and Radoslaw Majewski was sent off.
But they hauled themselves level through David McGoldrick’s fortuitous strike and defended heroically as the npower Championship leaders cranked up the pressure after the break.
Davies had no complaints about the red card shown to Majewski for an ugly lunge on Adel Taarabt, and instead praised the players who stayed on the pitch for their efforts.
“We had to play for 70 minutes with 10 men and when you work hard all week on your shape and that happens, it’s a disaster,” he said.
“I don’t think there can be a complaint, it’s a clear airborne challenge. It was naive and stupid.
“But even with 10 men we looked dangerous and we deserve credit after our game plan was blown to bits.
“My back five were magnificent. It’s a great point and a well-deserved one.”
Rangers sit six points clear at the top and remain on course for a return to the Premier League.
But manager Neil Warnock was unhappy when Matt Connolly conceded the free-kick which led to Forest’s equaliser and also felt referee Mark Clattenburg could have given his side a late penalty when Wayne Routledge went down in the box.
“There’s definitely contact,” he said. “But let’s be fair, I wish we had referees like that every week. Today’s game won’t decide our fate, the 15 we have left will.”
Cardiff, Norwich and Swansea all scored late goals on Saturday to boost their respective bids for automatic promotion.
Third-placed Cardiff had to wait 85 minutes to break the deadlock at home to lowly Scunthorpe, Seyi Olofinjana heading the only goal from Jason Koumas’ cross.
Norwich, who kicked off in fourth, led Reading when Arsenal loanee Henri Lansbury tucked in a cross from Wes Hoolahan, but 10 minutes later a mistake from Elliott Ward allowed Jimmy Kebe to set up in-form Ireland striker Shane Long for the equaliser.
Jem Karacan was sent off for the Royals after his wild tackle on David Fox sparked a mass melee and Norwich, as so often this season, grabbed a late winner as Grant Holt turned in Andrew Crofts’ cross in the fourth minute of stoppage time.
Fifth-placed Swansea came from 3-1 down to edge out Middlesbrough 4-3. Craig Beattie’s injury-time half-volley earned the Swans a dramatic three points.
Leeds are also in the hunt and they beat Bristol City 2-0 as Robert Snodgrass scored his seventh goal of the season and then set up Max Gradel.
Burnley moved above Millwall and boosted their play-off push courtesy of a 3-1 win at Watford.
In-form Hull made it seven league games without defeat as Anthony Gerrard earned them a 1-0 win over Preston.
Portsmouth ended a 10-match winless run with a 2-0 success at Doncaster. Dave Kitson headed his sixth goal of the season and Joel Ward wrapped up victory.
Struggling Crystal Palace went down 2-1 at Coventry.
Jacob Mellis’ stoppage-time equaliser earned Barnsley a draw at home to Ipswich, for whom Jason Scotland had broken the deadlock in the 82nd minute.