However, after being knocked out of the Scottish Cup by First Division side Raith Rovers on Tuesday night, the former Motherwell boss was spat upon by angry Pittodrie supporters as he made his way to the dressing rooms.
The Celtic manager has been subject to criticism from some Hoops fans as their Ibrox rivals have opened up a 10-point gap in recent weeks but he was taken aback by news of the physical abuse that McGhee had to endure.
Speaking ahead of the visit of Dundee United, he said: "That's a shocking thing you have just told me.
"I didn't know that was the case but I don't think anyone has the right to spit on anyone else.
"Managers are all hard-working guys.
"I sat with Mark after the game and from being dead and buried they came back to get a point so emotionally he was quite high and excited.
"And yet there you go, three days later he is having to suffer that - welcome to football management.
"It is a tough job.
"The days when you play really well and score goals are great, the days when it ain't going so well is when you find out about your players and find out about yourself."
While Mowbray knows that one more slip-up could take the title out of his reach, the importance of Champions League money to the Old Firm was highlighted again just this week.
Failure to qualify for this season's tournament was reflected in the Parkhead side's balance sheet which showed a decrease in turnover of almost 23% for the six months to the end of 2009, while bank debt increased from £0.97million to £3.13million.
Conversely, by qualifying for the tournament as champions, for the same time period Rangers posted a profit of just over £13million.
Yet more pressure is set to heaped on both Old Firm clubs with the news that Scotland is set to lose one of its Champions League places.
From the 2011/12 season, only the SPL title winners will have a chance to participate in the lucrative group stages which are generally thought to be worth £10 million.
However, Mowbray appeared relaxed about the issue of finances.
He said: "Whilst it is important for me to be successful, the Champions League is for the supporters coming to see our team compete against the best teams in the world, not necessarily about the millions that come with it.
"And yet the millions that come with it help bring players and the perpetual cycle continues.
"But it doesn't change my goal on wanting to build a team that the fans will be excited about, whether you wheel and deal with the resources that you have now or have £10million to spend.
"I don't know what finances would be available but we are constantly scouring the world for players and there is enough evidence to suggest that you don't have to spend £10million or £20 million to get some good football players.
"I like to think I have done that in the past and I'd like to think that's part of the reason we are at this club.
"We can identify talented players and put them together in to a team that can function.
"I am pretty sure that we are down the road to building long-term success."