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Although there was success come May, Celtic endured problems on and off the field last season.
O'Neill was brought out of retirement following the acrimonious departure of Rodgers and then was recalled for a second stint in interim charge after Wilfried Nancy's short-term spell as manager.
The club's supporters protested at length over a perceived lack of spending and the failure to reach the Champions League after defeat to Kazakh side Kairat Almaty.
That disgruntlement has carried over into this summer after chief executive Michael Nicholson said the transfer market was proving "difficult" because Celtic are competing with English Championship clubs for players and dealing with agents.
"There were obviously a few circumstances that made it more challenging than perhaps it has been in the past few seasons," McGregor said when asked about last season.
"You have to make sure when you face those challenges, you can overcome them. The group of boys and the staff that pulled the team through a really difficult season - that's what you need to build.
"Good characters, people that are willing to go to the death for each other.
"This season hopefully we can do it in a bit more style, the way that we're used to.
"Work's been going on through pre-season to make sure that happens."
As McGregor hinted, it will be a new-look Celtic squad that takes to the field in the coming weeks and months.
Influential Japan forward Daizen Maeda has left to join Premier League Ipswich Town, while striker Kelechi Iheanacho turned down a new contract at Celtic and instead signed with Turkish outfit Bursaspor.
Goalkeeper Kasper Schmeichel has retired, while loanees Marcelo Saracchi, Julian Araujo, Tomas Cvancara and Benjamin Arthur have all returned to their parent clubs.
However, Camilo Duran and club-record signing Kasper Hogh - both of whom have Champions League pedigree - have been brought in to bolster O'Neill's forward line.
