The Frenchman was only appointed on 3 December but has overseen six defeats in eight games in all competitions.
Rangers have overturned a nine-point deficit to Celtic in that time to move level with their Glasgow rivals and just three points behind leaders Hearts.
A dreadful run of results since Nancy's arrival is just the latest bone of contention for many in the Celtic support, as thousands gathered outside after the game, calling for a boardroom change.
"Nothing changes," Nancy told Sky Sports on his future. "My focus is to help my players to be better to turn things around.
"We are really close to doing good things, but the way we concede goals sometimes it is difficult."
The former Columbus Crew coach pleaded for time and patience in an impassioned rant on the eve of the game and initially got a response from his players.
Celtic had dominated the first 45 minutes and led through Yang Hyun-jun's solo run and blistering finish.
However, it was a completely different story after the break as Youssef Chermiti doubled his Rangers tally within nine minutes.
The Portuguese striker has been much maligned for wasteful finishing since his £8 million move from Everton in September.
Chermiti tapped in Nico Raskin's low cross to level and then sprinted clear of a static Celtic defence to slot past Kasper Schmeichel.
Tottenham loanee Mikey Moore then fired into the far corner to spark fury among the Celtic support.
"It is a statement. It's a massive three points, but now it's about continuing our way," said Rangers boss Danny Rohl, who has won nine of his 12 league games since taking charge in October.
The Celtic hierarchy have been under pressure all season for a perceived lack of investment in the playing squad.
But their decision to hire Nancy in the middle of a packed festive run of fixtures is now open to question.
With 18 league matches remaining, the Celtic board must decide whether to stick with their Nancy gamble or twist on another managerial change.
Celtic have won 14 of the last 15 Scottish Premiership titles, including the previous four.
But that run is in severe danger with Hearts aiming to end the Old Firm's 40-year stranglehold and a resurgent Rangers looking to take their crown.