But this hard-fought and deserved victory ensures everyone will stick to the party line today.
There have been too many times over the years when the Aberdeen players and supporters would have shown their frustration in games like this when their dominance failed to bring reward.
But attitudes, both on and off the pitch, have changed under the management of McInnes and he insisted last night that he was not over worried by his side's lack of goals in such a one-sided affair.
Ryan Jack produced the winner with less than 20 minutes remaining and collected the points that keeps his side on course for a second-place finish in the SPFL Premiership and it was enough to satisfy his manager.
"Having worked with these boys for the best part of a year I wasn't concerned," McInnes said. Coming hard on the heels of last weekend's cup triumph over Inverness Caledonian Thistle at Parkhead where a penalty shoot-out won the day for the Dons, McInnes remained convinced a winner would emerge over a Kilmarnock side which was pummelled into submission.
"The fans didn't get agitated and neither did we," he added. "That's because they have confidence in the team and we have confidence in ourselves."
Yesterday's victory over a Kilmarnock team bruised and battered for the large part of proceedings, set up Aberdeen for another big day today.
"The players were still getting congratulations before the game," added McInnes. "So as much as I've gone on about keeping focused, it could have been a problem. But I didn't think it would be an issue and was confident they'd deal with it."
It was indeed a day boasting a sense of occasion. You don't win a trophy for the first time in 19 years and not make a stellar production of your next home match, including a pre-match rendering of Peter Pawlett Baby, an unlikely chart hit. The memory of that League Cup win was still vivid in Aberdeen minds so milking it was always an option. And why not?
But, as with many parties, there is always someone ready to burst the balloon. Kris Boyd assumed the spoiler role, aided and abetted by Rory McKenzie, whose long, unimpeded run in the 12th minute ended with a tight pass to his team-mate whose strike was low and out of the reach of goalkeeper Jamie Langfield to earn him his 19th strike of the season.
The silence of the home support lasted only six minutes when Adam Rooney, whose penalty kick proved decisive last weekend, accepted Low's short pass before drilling the ball home from the edge of the area to restore parity. It was a deserved leveller given Aberdeen's dominance of a first half lacking in bite, though Niall McGinn's two opportunities from six yards, both of which missed the target, were worrying moments for the fans wearing red and white.
In a second half that failed to live up to expectations, Kilmarnock side were forced on to the back foot for long spells, able only to rely on the occasional counter to produce any kind of hope of worrying Langfield.
There was a weariness, too, among their overworked defenders as their management team wondered how long they could hold out. They were given that answer in the 72nd minute as Andrew Considine's low free kick crossed the goalmouth passed-by a few legs before Jack stepped in and broke the deadlock to leave the visitors reeling.
Allan Johnston's side now find themselves facing a scrap to keep out of the end-of-season playoffs. "We frustrated them for long periods," he said, "and we looked dangerous on the counter. So there were some pleasing points for us. But when you get yourselves in front against a quality team like Aberdeen then lose the second from a free kick, it's very disappointing. We are where we are because we lose too many goals, but we have a lot of big characters in our team and they can make a difference."