Davies was one of three defenders missing from the 1-0 defeat at Nottingham Forest, with Cristian Romero and Micky van de Ven also sidelined, but Spurs' issues were compounded when Radu Dragusin limped off with an ankle problem in the 87th minute.
Given the extent of the club's injury list, which also includes first-choice goalkeeper Guglielmo Vicario, Postecoglou conceded it may need to look to the transfer window to alleviate some of the issues.
"We're running a fine line," Postecoglou said. "There's always been issues at different times, but not to this extent.
"I think we've had close to pretty consistently 10 first-team players not available for a significant run of games. Definitely a first for me. We're in a tough spot, and we have been for a while.
"We've been kind of getting through it for quite a while and keeping our fingers crossed we don't get any more issues.
"[Transfer policy] can be disciplined, but we need a clear picture of where we're at. There is a need to reinforce if we can. It's not an easy time to do that in this window.
"The club is working hard behind the scenes to help the players we've got, who are giving everything in every game to try and get us through.
"We need to help some of these guys, because there's at least two or three who are feeling long-term injuries, so we're going to be short there. Others are coming back and need time to get up to speed. We're working hard to try to get reinforcements."
Against Forest, Spurs averaged more than 65 per cent possession for the seventh time in the Premier League this season, but they have lost five of those games.
Their defeat at The City Ground was their ninth in the Premier League this season, leaving them 11th on the table and 10 points behind rival Arsenal in fourth.
They now face Wolves at home, where they have conceded 31 goals in the league in 2024, the most Spurs have shipped in a single calendar year since 2007, when they let in 34.
With a Carabao Cup semi-final against Liverpool to come in January, Postecoglou insisted he still feels support from the fans, despite the increasing pressure.