It is a term, in truth, that has marked his career both as a player and as a coach. In his first match with Norwich City, after joining them from Celtic in 1997, Grant admits he almost became involved in a bit of "fisticuffs" in the dressing-room.
His problem was that his team-mates were celebrating a 1-1 draw away to Stoke City. "The other players were singing, dancing and laughing about it. I couldn't believe it. Drawing any game wasn't acceptable to me but the manager took me aside and said that down there any point away from home is a fantastic result," Grant said.
The midfielder, in contrast, was accustomed to the "intensity "of playing for Celtic, where victory was demanded every week. He said this quality can forge players but it can also mark managers.
There have been glances from English clubs in the direction of Neil Lennon after Celtic's success in qualifying for the last 16 of the Champions League but Grant, who has managed at Norwich and coached at West Ham United and West Bromwich Albion, pointed out there may be a dilemma for the Northern Irishman.
"The intensity of managing Celtic or Rangers is different from anywhere else. I have been down south for 15 years and know that the mentality is completely different," said Grant, now 47. "At the moment, is Neil going to get a Man Utd or a Man City? I don't think so. So is he going to go a smaller club and make his name from there? I'm not so sure. Maybe the pressure and intensity of managing Celtic is what keeps him going."
Grant, who played more 300 games in a career at Celtic that stretched from 1982 to 1997, added: "Could Neil work without that intensity? I don't know, that's the question. If he went down to England and it didn't work would people say he was a failure? It would be frustrating for a manager who has worked with the Old Firm to then go to a club where players don't have the same drive every day.
"From a player's point of view it was draining so it must be multiplied tenfold when you are the manager. There is a huge expectation and this season Neil has a different kind of pressure because there's no Rangers. People are saying they expect Celtic to win the league by 30 points and that itself brings a new kind of intensity.
"As a Celtic or Rangers manager you don't get a moment away from it. Maybe that's the thing that does make him move out the door, who knows? But if an offer was to come in it would be a huge decision for him because there's not many bigger clubs than Celtic"
Grant, though, insists the demands on the current Celtic players will have made them attractive to clubs in the Barclays Premier League. There has been speculation linking Victor Wanyama, Gary Hooper, Fraser Forster and others to top-flight English clubs and Grant revealed he had scouted the striker for West Brom and was surprised at the progress he has made at Celtic.
"Did I think he would have achieved what he has at Celtic? Probably not," he said of Hooper. "I always thought he would score goals; he will score in any team if he gets chances. For England, Roy Hodgson is a bit more defensive so he would maybe find himself getting fewer opportunities. But he's definitely worth a shout for England."
And the price tag of the striker signed from Scunthorpe for £2.2m? "Jordan Rhodes went for £8m after scoring goals in League One. Gary Hooper is doing it for Celtic in the SPL and in Europe so who knows what he's worth? He's been doing it week-in, week-out for a big club like Celtic so he could go anywhere after sampling that intensity."
And his verdict on the Kenyan? "Wanyama could play in England, no question."
He is similarly assured of the worth of Forster. "Few people would have known about him prior to the Champions League but they all know who he is now," said Grant. "Celtic's problem is going to be holding on to these boys because they have done so well. Attracting players is going to be difficult."
The former Celtic player believes his old club will now be re-assessed by potential opponents in Thursday's draw for the last 16. "The other clubs will be looking at being drawn with Celtic as a difficult occasion," he said after the Parkhead club finished second behind Barcelona in Group G. "They will be looking at it differently now compared to a few months ago. If you ask Manchester United if they want to come to Celtic Park, with the intensity that goes with it, then they'd probably say no. There would be more of a fear for them because they would be expected to beat Celtic.
"Celtic are in a good position at this moment in time, they are a team people will want to avoid."
It is a verdict delivered with certainty, and no little intensity.
n Peter Grant and Alex McLeish were speaking to promote ESPN's festive coverage of the Clydesdale Bank Premier League and the Barclays Premier League