Mowbray walked tall into his first press conference at Celtic Park on Wednesday as the new Hoops' boss, but it was a wonder given the expectations that have been heaped upon the shoulders of the former Parkhead defender.
Despite leading West Brom to relegation out of the Premier League last season, Mowbray arrived in the east end of Glasgow, where he played for four years in the 1990s, heralded as something of a Godfather of free-flowing, attacking and entertaining football - the type that Celtic fans believe to be their birthright.
The recently departed Gordon Strachan, despite winning three Scottish Premier League championships in succession, three domestic cups and leading the club to the last-16 of the Champions League two years running, was constantly harangued by a section of the support for not playing the 'Celtic way' during his four-year tenure.
Those fans got their wish three weeks ago when Strachan called it a day after failing to win his fourth SPL title.
The 'Celtic way' mantra was repeated in all media outlets by fans, former players and pundits in the intervening period as the DNA of Strachan's possible successor was analysed.
Most pointed back to Tommy Burns' spell as Celtic manager between 1994 and 1997, when, for a short period, the 'Three Amigos' of Pierre van Hooijdonk, Paolo Di Canio and Jorge Cadete personified what has become almost a halcyon time for some Hoops supporters.
Of course, the reality was somewhat different.
Burns' teams could not prevent Rangers marching on to equal the Parkhead side's record of nine titles in succession - it would take his successor Wim Jansen to prevent the Ibrox men taking it to 10 - and there were some embarrassments during that time, not least the Skol Cup final defeat to Raith Rovers at Ibrox, and routine defeats by PSG and Hamburg in Europe.
Only a Scottish Cup was captured and so Burns had to go.
Mowbray, the 16th man to manage Celtic in the club's 121-year history, was flanked by chairman John Reid and chief executive Peter Lawwell as he surveyed the media ensemble eager for him to outline his plans.
He sat there knowing a Scottish Cup final victory in the next three years will not suffice.
His time at Hibernian was decent with two top-four finishes in the SPL. When it was good at Easter Road, it was very good - but when it was bad, it often looked terrible.
Mowbray twice left Ibrox with handsome 3-0 wins which will encourage the Parkhead faithful, but for the debit column, Hibs capitulated spectacularly in a Scottish Cup semi-final to Edinburgh rivals Hearts at Hampden.
At West Brom he enhanced his reputation for playing attractive football but his reward was relegation.
The big Teessider often highlighted a lack of resources at both Hibs and West Brom but in a Scottish context, that is no longer the case.
He is with a club who simply have to win trophies - and whose fans now expect them to be won the Celtic way.
As Mowbray spoke with his trademark enthusiasm, he failed, for the most part, to dampen down those expectations.
While claiming that his reputation for preferring style over substance was a "fallacy", he did little to dissuade the green and white hordes that they were not about to join him on a Utopian football journey.
He talked about the need not only to win, but to entertain the fans.
He explained that he planned to build a team to be feared in Europe again while making oblique comparisons with Champions League holders Barcelona.
So, no pressure there then.
Time will tell if the pressure to take Celtic on to a higher footballing plane will be a burden. But perhaps not a lot of time.
The Parkhead club, by dint of their second-place finish in the SPL last season, face the first of possibly two tricky Champions League qualifiers at the end of July.
Mowbray's last foray in to Europe saw him lose 5-1 away to Dnipro in the UEFA Cup with Hibs, following a goalless draw at Easter Road.
His predecessor, of course, infamously lost 5-0 to Artmedia Bratislava in his first game in charge of Celtic which ultimately ended the Parkhead side's European hopes for that season.
But Mowbray would be well advised not to use that as a guide.
As the 30-minute press conference drew to a close, a couple of Celtic fans sitting at the back took the opportunity to wish Mowbray all the best.
One of them declared: "Can I just assure you of 100% backing from the Celtic supporters.
"We won't be looking for anybody's head after three games."
Inadvertently, it could be considered as much a warning as a