The Swede claims that Celtic have also suffered as a result of Rangers' financial meltdown.
Hoops manager Ronny Deila has come under fire in recent weeks and months as the reigning Scottish champions appear to be making rather hard work of what could and should have been a one-horse race this season.
Aberdeen sit just one point behind Celtic in second as Derek McInnes's side threaten what would have seemed an unimaginable upset way back in August, but it seems very realistic at the moment.
Overall, Celtic have struggled to fully capitalise on Rangers' demotion to the fourth tier back in 2012 and monopolise the Scottish game, and Mjallby claims the financial meltdown has not been positive for either Old Firm club.
“I think Celtic have not pushed on in recent times and have actually gone backwards because of the fall of Rangers," he told Bwin.
“Obviously the Old Firm matches gave the clubs more TV money and I think Celtic have suffered from not having Rangers there to push them. If you have a massive rival, where you know you can’t lose any points or hold up, then you perform better.
“Now, with Rangers out of the picture, Celtic have lacked the competition and they have suffered in the Champions League as a result of that because they don’t get punished domestically how they do in European competitions."
Mjallby is almost certain to get his wish next season as Mark Warburton's men sit top of the Scottish Championship, 14 points clear of Falkirk in second.
Barring a minor miracle, the Ibrox club will be back in the big time by August, and Celtic, whether they win the title this season or not, will have to pull their socks up.