The Ibrox side drew the second leg of their third qualifying round tie against Jagiellonia Bialystok 1-1 at Ibrox, but crashed out 3-2 on aggregate.
It is their earliest exit from the competition since 2017, as McInnes' winless start as manager of the Ibrox side stretched to four games.
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The Rangers fans made their feelings clear at full-time as boos rang around the stadium, something McInnes accepted.
"It was justified, to be honest. It wasn't good enough. What we served up, particularly second half, wasn't good enough," the former Rangers midfielder said.
"We need to be honest, the club's built for Europa League and Champions League and that's the intention, to get there.
"But I'm not sure the team is quite ready for it at the moment and it pains me to say that, to be honest, it does.
"We need to get more quality, we need to try and get more confidence out of the team."
Missing left-back Tuur Rommens and striker Youssef Chermiti through injury, McInnes moved to a back three among five changes from Sunday's defeat by Hibernian.
"I felt we had to make the game open and it was a bit too open at times in the first half. Gassama and Yakota playing as kind of effectively wing-backs, we were asking a lot of them at times," he added
"But I thought it paid dividends in terms of penalty box action, getting the goal.
"I thought we were good value for getting it one and a half-time, but I still thought that Jagiellonia had a couple of scares.
"Once again, it's not another 90-minute performance.
"That's been in the Rangers for a while now. It's been a continuation of that this season, already.
"In the four games we've played, we've had some good moments, but it's not been good enough and certainly not a strong enough 90-minute performance.
"But for us to lose the goal. It's inexplicable how we don't make a foul, how we don't stop the flow of the attack, how we don't just sanitise that whole situation.
"It's not lack of bodies, it's lack of intelligence, it's lack of doing the right thing, to be honest.
"We lost all our composure after that, if I'm going to be honest with you.
The 55-year-old is Rangers' sixth permanent manager since Steven Gerrard left the club in 2021.
Despite making a dismal start, he remains confident he can turn things around.
"What we served up last year wasn't good enough. You get a job for a reason," the former Hearts head coach said.
"You get a job to try and make things better and obviously sometimes you get it because things aren't quite right, and we have to try and get things moving the right way quickly.
"There's no two ways about it, we should be winning this game.
"Rangers, as strong as they can be, should be winning this day and we have got work to do between now and the end of the window, but between now and Sunday to get ready to win a [League] Cup tie [against holders St Mirren]."
