Celtic's new manager will need to find some dramatic improvements, and quickly, before things unravel in front of his eyes in just his first couple of weeks in charge.
His decision to stick with the same starting XI who lost to Hearts backfired, with one of Celtic's worst first-half performances in recent memory. It would be hard to overstate the manner in which they were totally outplayed.
Three cheap goals goals conceded. Numerous other chances afforded. A really good Kasper Schmeichel save. The failure of record signing Engels to hit the target with a penalty.
Fielding only three defenders in each of his first two games has brought nothing but pain for Nancy, who seemed content to let the first period play out even when it was very clearly not going to plan.
If he's stress-testing his players, several have failed. Using wingers Yang Hyun-Jun and Sebastian Tounekti as the last line of defence in wide areas to accommodate his 3-4-3 system is surely unsustainable.
Roma were streets ahead in every department, despite coach Gian Piero Gasperini opting to leave Bryan Cristante, Lorenzo Pellegrini, Kostas Tsimikas, Manu Kone, Paulo Dybala and Wesley on the bench.
What the Italian giants might have done to Celtic with their best side on the pitch barely bears thinking about.
As lessons go, this was a sore one. As learning curves go, this is as steep as it gets for the new Celtic manager.
Two big games, two damaging defeats, both at a disbelieving Parkhead, where frustrated fans are looking for reasons to vent further at the club's heirarchy. St Mirren will approach Sunday's League Cup final with optimism.
Celtic's players who look like a shadow of those who Martin O'Neill steered to seven wins out of eight and Nancy will have learned plenty about them.
The changes he makes for the Hampden showpiece - assuming he makes any at all - could determine whether he's holding silverware at the end of his first full week in charge or holding his head in exasperation at a start out of his worst nightmares.