Twelve years on, the giant Swede is again a key figure in the quest to better that total of 18.
Neil Lennon's trusted right-hand man is now what other sports might refer to as the defensive co-ordinator.
And you only need to watch him in the technical area go from cool Scandinavian to whirling dervish if the men in the Celtic back line make a mistake to understand how seriously he takes his responsibility.
There were a few too many of those animated moments for his liking in the first part of the season, when 12 goals were shipped in the opening 13 SPFL games.
However, when all the work being done to make the Virgil van Dijk/Efe Ambrose combo - which was formed last summer - finally clicked, the results were there to see.
With Fraser Forster also on the very top of his game, the goals-against column appeared to be frozen in time.
In fact, it has only risen by two since November 23.
Eventually, a new consecutive league clean-sheet record for Celtic - then for Scotland - was set.
The spell they held over the opposition strikers was finally broken last month by Jonny Hayes' wonder goal for Aberdeen at Pittodrie, with Adam Rooney slipping in to score a second later that night.
But since that double disappointment of losing goals and all three points, the Hoops have got right back on the clean-sheet trail.
Now they have the record for least goals conceded in a season very much in their sights.
Celtic have lost just 14 in 29 games, less than one every two matches - a huge improvement on the 35 they shipped during last term's campaign.
Now they can afford to concede just three more in the closing nine games if they are to beat the 2001-02 record.
And, working with the defenders every day, Mjallby can sense they are determined to make another entry in the history books.
As he watches Van Dijk and Ambrose repel virtually all raiders, the former Swedish international admitted: "I do take a lot of pride in that.
"To be successful, you always have to have a strong backbone to make it easier for the guys to make it happen going forward.
"We were a bit disappointed last year because we conceded too many for our liking.
"This season, we have been very, very consistent, and haven't conceded many.
"It's not only the defenders, of course. You also have to praise Fraser Forster. We have been strong in that department. "
Mjallby believes there is a real bond between the players, a unity which is reflected in their performances, and which helped them get back on the shut-out track when they were derailed at Pittodrie the night Van Dijk was shown red.
"We had a great clean-sheet run," he explained. "Then, in the end, we conceded a great goal at Aberdeen, which was always bound to happen.
"Maybe it was a little bit too much to hope we could go on with the not-conceding-any-goals run. Maybe we thought too much about it.
"But, at the same time, Virgil got the red card and it was obviously a great goal which Aberdeen scored."
Mjallby, as ever, is philosophical about the disappointment, and keeps everything in proper perspective.
"The most important thing is to win games," he said. "If you concede a goal here and there, it doesn't matter. But it is important to have a strong backbone.
"Maybe that is due to the fact most of the guys have not been injured. We haven't chopped and changed much in the defensive department. It's great for you to know who you play with, and you get a great understanding."
The defence which Mjallby played in under Martin O'Neill was based on three physically-imposing centre-backs - think Bobo Balde -who rarely left their station.
They relied on wide midfielders in the 3-5-2 formation to bomb forward, but get back to provide cover when required.
The current system is very different to that, and reflects the need these days for central defenders who are much more comfortable - and effective - on the ball.
It took a while to find the men to fit the identikit, and the loss of Kelvin Wilson last summer appeared to set the plan back as he was a key element in the defence Lennon was trying to build for the future.
But the discovery of Van Dijk has changed things back in Celtic's favour, and the partnership with Ambrose has come together faster and better than anyone could have reasonably expected.
That's apt, given how important speed is to the way this team defends.
"The way we see the game, we want to have pace in the centre of the back line," Mjallby told Celtic TV. "Efe is blessed with great pace, and Virgil is no slouch, either."
Something which makes the Dutchman a very hot property after just 10 months in the Hoops.
Mjallby shares the admiration reputedly being shown by top managers in England.
"Virgil is just a top, top player," he said. "He can play with the ball, also. He is really clever, he can go forward, and he has the physique as well and is good in the air.
"Virgil and Efe communicate well together and know each other now. Virgil has been a great find for us, and he is going to have a wonderful career."