Neither Russell Martin nor Danny Rohl were able to restore past glories in their short stints in Govan while McInnes was taking Hearts to the verge of immortality.
Much of the condemnation surrounding the Ibrox club’s failures last season came back to the same theme – they may be fluid and clinical going forward at times, but a soft underbelly put paid to hopes of success.
“I thought we gave up too many chances and gave teams too much encouragement,” the 55-year-old added post match in Poland.
“We’ve got to be honest and say we are guilty of beating ourselves tonight. And that’s no disrespect to our opponent because on transitions and counter-attack, it fuels them.”
Rangers were flailing in the opening 45 minutes as Jagiellonia cut them open with ease, capitalising on numerous lapses in concentration.
Twelve minutes into the game, Thelo Aasgaard tried an audacious spin on the edge of the hosts’ box, attempting to squeeze the ball through a small gap in the defence.
One minute later it was in the back of Rangers’ net following an impressive counter.
“There’s no bigger drain on confidence for any player, team, support than losing cheap goals,” McInnes said.
“There were mistakes for the goals, and I understand that can happen, but we have got to be far more stingy with our work, defend the goal with our lives, don’t give our opponent opportunities.
“At no cost is that ball going in our box, at no cost are they going to get a chance, and we’ve got to have a bit more of that approach to our work.”
The central defensive partnership of Dujon Sterling and Emmanuel Fernandez looked particularly shaky.
“If you spoke to McInnes right now without a microphone in front of him, and you asked him, ‘Do you trust Fernandez?’, there’s no way he says yes, no way,” former Rangers midfielder Andy Halliday said on BBC Sportsound.
“But he doesn’t have an option at this moment in time to play someone else.
“I’m being very critical here, but I think Fernandez has every attribute to be a top, top central defender, yet it looks as if he hasn’t had the education growing up of the basics of being a central defender.”