The Scottish champions crashed out on Tuesday after suffering a shock 1-0 home defeat to Morton.
But Aberdeen have cruised into Thursday's quarter-final draw after substitute Scott Vernon grabbed a hat-trick in a 5-0 win at Falkirk.
McInnes, however, insists his squad will remain level headed, despite clamour from their own supporters to end the Pittodrie club's 18-year wait for a trophy.
He said: "Everybody who is left in the tournament will see it as being quite open now that Celtic are out.
"But for me we just need to concentrate on what we are doing, regardless of what the draw throws up. Ideally we would like to be at home.
"I understand that there is so much expected from Aberdeen and I would never try to fan the flames of that.
"At the same time, we went a couple of games recently without winning a goal and it was the end of the world if you listened to some people.
"For us as a staff and a group of players, we will just keep an even keel on things. We can't stop what other people are saying but we are not kidded. There is work to be done."
Joe Shaughnessy fired Aberdeen ahead at the Falkirk Stadium after 22 minutes before Cammy Smith doubled the Dons' lead nine minutes before the break.
Vernon failed to find the net in the 15 minutes he played of the first half after replacing Calvin Zola on the half-hour mark.
The former Burton frontman was hooked as McInnes feared he might be sent off after collecting an early booking, but his replacement started the second period on fire as he blasted two goals in two minutes before claiming the match ball with a spot-kick after Will Vaulks bundled Peter Pawlett over in the box 17 minutes from time.
Aberdeen were simply fantastic going forward but their Championship hosts were all over the place at the back and Falkirk boss Gary Holt admitted his side played a significant part in their own downfall.
"I thought Aberdeen were really good but I thought we stood of them and let them play," he said.
"We looked like we got caught in this mindset that they are the Premier League side and we can't tackle them. Whereas every time we got the ball, there was one or two of their guys ratting about us.
"We try to instill in our players that we have to get after the ball but we didn't and it looked like men against boys."