McInnes watched on as his side were thumped by Steven Gerrard's rampant team at Ibrox.
He said: "Aberdeen, with our experienced, battle-hardened players, can still win these games. There is no question of that - but we looked miles away from that.
"We looked like a team playing our own wee game and we lacked the personality and experience you need to get a result at Ibrox.
"There was a lethargy about our performance after the extra-time against Hearts the other night. But we were also too passive at times and I'd expect more."
Following the Betfred Cup loss to Hearts on penalties on Wednesday evening the odds on McInnes being the first manager to leave fell from 10/1 to 6/1.
Now he is priced at just 7/4.
Hibs boss Paul Heckingbottom has gone from 7/4 to 11/4 after the draw with Celtic. A result which saw Neil Lennon's odds cut from 20/1 to 14/1.
Odds on the 12 Scottish Premiership managers to be the first to leave their post:
Derek McInnes (Aberdeen) - 7/4
Paul Heckingbottom (Hibernian) - 11/4
Craig Levein - 6/1
Tommy Wright (St Johnstone) - 8/1
Angelo Alessio (Kilmarnock) - 14/1
Neil Lennon - 14/1
Brian Rice (Hamilton Academical) - 16/1
Gary Holt (Livingston) - 20/1
Jim Goodwin (St Mirren) - 20/1
Stuart Kettlewell/Steven Ferguson (Ross County) - 20/1
Stephen Robinson (Motherwell) - 33/1
Steven Gerrard (Rangers) - 33/1