Rangers' exit came just 48 hours after bitter rivals Celtic surrendered a 4-0 aggregate lead against LASK to suffer their own agonising Champions League qualifying elimination.
Addressing his managerial culpability and his side's fragile mindset under pressure, McInnes added: "The best players can miss penalty kicks but we had enough time to get through the tie. The responsibility is shared tonight, but I'm responsible for bringing a better performance than what we showed tonight. And for that I'm embarrassed. I so disappointed that we've been emptied out of Europe.
"It's all about trying to work towards better performances and trying to win games of football. But we were way off, we have to be totally honest with that."