Celtic manager Gordon Strachan admitted sympathy for Paul Le Guen and claimed Old Firm bosses inhabit a 'fantasy' world.
Since arriving at Parkhead in the summer of 2005, the former Coventry and Southampton manager has seen off two of his Ibrox counterparts.
The Frenchman left after meeting chairman David Murray on Thursday only seven months after taking over from Alex McLeish.
Beleaguered Rangers, currently 17 points behind the Hoops in the Bank of Scotland Premier League, will try to pick up the pieces of a disastrous season with Scotland manager and former Light Blues' boss Walter Smith hot favourite to return to the helm.
Strachan was keen to stress the peculiar pressures under which he thinks Celtic and Rangers managers operate.
He said: 'If you can manage either half of the Old Firm without losing your sanity then you can go anywhere in the world.
'The physical and psychological toll that's taken of you by the time you leave depends on what kind of state the club's in at the time.
'The hardest part of working with the Old Firm is the fantasy that attaches itself to the clubs.
'By that I mean everything that is unreal. I can deal with my players and how we handle the opposition, everything else is unreal to me.
'So I can sympathise with Paul or any other manager when they lose their jobs because it's a hard business.
'Graeme Souness told me that when he was at Ibrox he knew the fight was on to keep hold of his sanity and he was right.'
Celtic take on Dumbarton at home in their Tennent's Scottish Cup third round tie today.
However, with the match not being part of the Celtic Park season-ticket book, the Hoops are likely to be playing in front of their lowest home crowd of the campaign.
Strachan is hoping his players can motivate themselves for the visit of the Third Division minnows.
He said: 'Obviously the build-up is not the same from a media point of view which is understandable.
'We've got to try and self-motivate because, if you talk about the Champions League and big games, the crowd, the build-up and enthusiasm take you along.
'So we have to do all this self-motivation thing and hopefully we get that right.'
Midfielder Shaun Maloney, out of contract at the end of the season, will meet chief executive Peter Lawwell next week to decide if he stays or goes.
Out-of-favour midfielder Alan Thompson has rejected a loan move to Leeds until the end of the season but is wanted by two other clubs.