The Tigers chief described his team as "excellent" going forwards, but conceded there was room for improvement at the back.
So, what better way for his players to respond than with a clean-sheet in addition to three superb goals, their 3-0 success lifting them to 11th in the table, just four points off the top six.
Saturday's defensive display probably warranted a shut-out and while McCann will doubtless have been delighted with the way City protected goalkeeper George Long for the most part, the quality of the three they bagged at the other end won't have been lost on him.
However, as good as City have been as an offensive unit this term, they haven't always made the most of the opportunities that they have created in front of goal.
And, for 45 minutes of an absorbing first-half at the KCOM Stadium it looked as if the same old story was about to unfold.
After Josh Bowler cut in off the right and saw an early effort deflected narrowly wide, the hosts conspired to spurn their first clear opportunity of the afternoon with 10 minutes on the clock.
Tom Eaves met a right-wing corner kick and directed a header towards the far post, where a stretching Jackson Irvine somehow failed find the back of the net barely a yard out.
Kamil Grosicki then crossed from the left and found Bowler in space inside the box, however despite taking a touch to set himself, the Everton-loanee got his finish all wrong.
Birmingham showed glimpses of their quality, but a long-range strike from Francisco Villalba which drew an awkward parry out of Long was about as close as they came to a breakthrough.
With the opening period seemingly destined to end goalless, Hull then forced what was their eighth corner of the match and got their noses in front.
Kamil Grosicki delivered from the left and Eaves made a run to the near post where he cleverly glanced a header over Connal Trueman for 1-0.
The early stages of the second period saw City again getting into dangerous positions without managing to profit from them.
Grosicki got in behind down the left, only to miss everyone with his pull-back, then Jarrod Bowen raced towards goal and could have slipped the flying Pole through, but delayed his pass too long.
A one-goal lead is never enough, and at this stage, one was still left wondering if McCann's men would be left to rue their lack of ruthless edge.
Then, just before the hour-mark, Bowen made a better decision than the one he took just two minutes previous, releasing the ball early and sending Grosicki in on goal.
What followed was a moment of genuine class, the former Rennes attacker speeding towards the onrushing Trueman before dinking the ball over him in sumptuous fashion.
From there on it, it was pretty much plain sailing for the Tigers, though the Birmingham should have pulled one back on 74 minutes when Jefferson Montero crossed from the left for Alvaro Gimenez to nod a great opportunity narrowly the wrong side of the upright.
That was about as good as it got for Pep Clotet's team and they were put out of their misery on 88 minutes as substitute Keane Lewis-Potter once again demonstrated what a talent he is by wrapping up the three points.
Picking the ball up inside the box, the 18-year-old local boy stood up marker Harlee Dean before confidently sending a finish low and hard across goal and beyond Trueman.
Happy Christmas, indeed.