Celtic closed their Champions League campaign with a 6-1 defeat in Barcelona this month after a three-point total failed to build on last season's campaign, when they reached the last 16.
But Celtic remain unbeaten in the Scottish Premiership and Mjallby wants that statistic to continue when they host Hearts on Saturday as they bid to atone for their disappointment further afield.
"It's always busy over Christmas and New Year so you're used to it and it's great in a way after the disappointment with Europe," the Swede told Celtic TV. "We have this unbeaten record and we have something to motivate the players with.
"And that's how it's going to be now, making sure the players are fully focused and keep progressing. Lately the performances have been very good and hopefully we can keep that up."
While Celtic excelled in Europe last season, they lost seven league games and Mjallby does not want a repeat of their domestic record.
"Last year the run we had in Europe was incredible and the players made us really proud, but we knew it might be a bit harder this year because it was a more difficult group," he said.
"After three games we were in a good position, and probably expected a wee bit more from the last three games in the group phase.
"But it wasn't to be so that's why it's important to be much more solid domestically this year when it comes to the league performances.
"We have players that we know can hurt other teams, and we have been waiting for a long time this season to see it really happening, but lately it's been great with free-flowing football - that's the way we want to play."