Neither Russell Martin nor Danny Rohl managed to revive former glories during their brief spells in Govan, while McInnes had Hearts flirting with immortality.
Much of the criticism of the Ibrox side last season centred on a familiar issue: they could look fluid and ruthless in attack, but a soft core ultimately derailed their ambitions.
After the match in Poland, the 55-year-old admitted they allowed too many openings and gave their opponents encouragement.
He said they largely beat themselves on the night—without slighting the opposition—whose transitions and counter-attacks were only strengthened by those errors.
Rangers were reeling in the first half as Jagiellonia repeatedly cut through them, taking full advantage of lapses in concentration.
Twelve minutes in, Thelo Aasgaard attempted a daring spin on the edge of the hosts’ area, trying to slip the ball through a narrow gap in the defence.
Sixty seconds later, after a swift counter, it was in the Rangers net.
McInnes noted that nothing drains confidence for players, teams, or supporters more than conceding cheap goals.
He accepted mistakes can happen but insisted they must be far more miserly, defend the goal with absolute commitment, and deny opponents opportunities.
He urged a mentality where balls are kept out of the box at all costs and chances are not given up.
The central-defensive pairing of Dujon Sterling and Emmanuel Fernandez looked particularly vulnerable.
On BBC Sportsound, former Rangers midfielder Andy Halliday suggested that, if asked privately, McInnes would not currently trust Fernandez, though he lacks alternatives just now.
He was highly critical, yet maintained Fernandez has the attributes to become a top centre-back.
Halliday added it appears the defender has not fully learned the basic fundamentals of the role despite his clear potential.