Indeed, Celtic boss Deila went on the defensive on Friday afternoon, telling reporters everyone outside of Parkhead wants to 'hurt' the Scottish champions.
The Norwegian also suggested Rangers face far less pressure while they are in the Scottish Championship.
But the former Aberdeen boss told BBC Scotland: "You would think Rangers will probably come back next season and they'll be getting stick from the beginning also if they're not in second or third place. Hearts, and Hibs if they get back, will be the same. They're all big clubs.
"Ajax got beat by Feyenoord, their big rivals, and they will get absolutely slaughtered by the papers in Amsterdam. Frank [De Boer] will be getting it. You look at Feyenoord, I don't think they've won the league in 15 years, they'll get it also.
"Every big club, certainly the biggest three clubs in the competition, will get stick."
Is Deila's outburst a sign that he is cracking under the pressure?
Or is the Celtic boss simply sending out a strong message that he plans to back up with a series of victories when it matters?
What will be interesting is to see just how Rangers cope if promoted to the Scottish Premiership next season - and if Calderwood's claims are true.
They likely are and both Celtic and Rangers will face as much pressure as each other when they lose. For now, all Deila has done is attract further attention and scrutiny to both the Bhoys' and his own performances over the next few weeks.