After the best season of his career, verified by a clean sweep of the Player of Year awards, the Celtic defender wants to do even better this time around.
He accepts it is a big ask. However, the 26-year-old player can take a giant step towards achieving his personal goal if he can help the Parkhead club avoid an early exit from Europe and set them on the road to the Champions League group stage.
Mulgrew needs no reminding how difficult that can be. For the past three seasons, he has suffered qualifying round despair, starting with Aberdeen when he scored their only goal in an 8-1 aggregate defeat to Czech side, Sigma Olomouc, in the Europa League.
When he made his surprise move back to Celtic, his first game was in the 3-0 Champions League qualifying round defeat in Braga. Neil Lennon's side did manage to win 2-1 in the return, but still dropped down to the Europa League knockout round, where Utrecht turned around a 2-0 first leg deficit to send Celtic out of Europe for the season.
Last year, it was Sion who inflicted the early-season pain, drawing in Glasgow before sending Celtic reeling with a 3-1 win in Switzerland, Mulgrew's goal doing nothing to ease his personal disappointment.
Only the fact that Sion were subsequently thrown out for fielding ineligible players allowed Celtic back into the competition and finally gave Mulgrew the opportunity to enjoy a European campaign of some duration.
This time around it is HJK Helsinki, provided they do not suffer a cataclysmic collapse in their second round, secong leg tie against KR Reykjavik this week, who will present the first hurdle to Celtic's qualifying ambitions.
Mulgrew, who will face no further action after being sent off in last night's 4-0 defeat to Ajax, confesses he knows little about the Finns who have won the Veikkausliiga for the past three years, but who are currently struggling to find that form as they pursue a fourth title.
"It's nice to know who we're playing," said Mulgrew. "It gives us a focus now that we know who we have to beat to get to the next round.
"I didn't look at who we could have got, or what would work out well for us. It could have been worse. But we knew it was never going to be an easy game and that we would have to prepare right, no matter who it was."
Helsinki represent everything manager Lennon did not want from this draw. The timing of the tie is his main concern, and the fact Helsinki will have 19 league games under their belt when they come to Parkhead next midweek means they will be well into their stride while Celtic are still using pre-season matches to find theirs.
This continues with the home games against Norwich on Tuesday then Inter Milan on Saturday, and Mulgrew said: "I'm sure, with the number of pre-season games we have, we'll be prepared and all up to sharpness by the time Helsinki come to Glasgow. It's not hard once you have played a few games."
What will be tough for Mulgrew is the aim of topping those achievements of last season. However, he is not prepared to rest on his laurels. He said: "I had a good season, personally, and I have just got to look to do better. I just try to stay focused, or maybe the confidence I gained from last year will make it better again. Maybe I never thought that last season would be as good as it was. But I do believe in my ability."
Which will be tested to the nth degree if Celtic can make it into the Champions League proper and give Mulgrew the chance to play in that competition for the first time. He acknowledges that, with the loss of Old Firm games, competing against the best Europe has to offer will be even more important to the Celtic.
However, the prospect of reviving Celtic's falling co-efficient rating and re-establishing the club among Europe's elite is what is providing the focus for Mulgrew.
"The Inter game will give us a marker of where we are in terms of Champions League football," he added. "We have a settled team, and there is good morale among the squad. That can only help us."