Yet the Dons can point to their lofty Premiership position alongside their visitors, who only nudge in front at the top of the Premiership table on goal difference, as testament to their desire to maintain their challenge.
The manager has steered his side to a nine-game unbeaten run which has been achieved without them delivering the kind of pulsating performances that were on show last term, having lost quality players such as Jonny Hayes, now at Celtic, Niall McGinn, plying his trade in South Korea, and Ryan Jack, now at Rangers.
McInnes would have liked to have had his squad in friendly action in the past few days, given that their last game was the 1-0 win over Hibernian at Easter Road eight days ago.
However, he does not believe Celtic’s two-games-in-four-day schedule, last Wednesday against Bayern Munich in Germany and yesterday’s Betfred League Cup semi-final, will have an adverse effect.
In the back of his mind, however, is the fact that Aberdeen were unable to prise a single point from Celtic last season as well as the memory of losing two cup finals to them.
“Being unable to take anything from our games against Celtic last season is not something that sits well with us,” McInnes admitted. “But it’s a new team for us with new players and a new season. We find ourselves at the top of the table with them again but they are still the team to beat.
“Every game against them is a challenge. All managers would say that every time you come up against Celtic it’s the biggest challenge but we don’t want a similar record against them this year as what we had last season.
“I firmly believe we are capable of beating them but for Celtic to be unbeaten domestically last season and to have been so convincing deserves a lot of credit.
“It also shows the task ahead of us but it is important for us to try to beat them this season.”
McInnes shrugs off suggestions that Celtic will still be reeling from their filleting by Bayern in the Champions League. They are too professional for that, he says.
“Celtic will see their challenge is now with Anderlecht,” he said. “I think they’ll win that fight and qualify. When you are used to working at clubs like Celtic and you have a squad full of international players, they’re used to having big demands on them.”