Dailly played alongside McCulloch during his own brief spell at the Glasgow giants and saw at close hand just how much achieving success mattered to the lifelong fan.
The utility man was an influential player in the great Gers side that bounced back from last-day disappointment in 2008 to land the Scottish title in the final game in 2009.
Dailly was not surprised when his old Scotland team-mate chose to stay at Rangers when so many others moved on to new clubs when they dropped into the Irn-Bru Third Division this summer.
Ally McCoist's young side produced another poor display away from home against Forres Mechanics in the second round of the William Hill Scottish Cup at the weekend.
The unconvincing 1-0 win over the part-time minnows came after disappointing showings against Brechin City, Peterhead, Berwick Rangers and Annan on the road.
But Dailly believes having the vastly experienced star at the club will ensure the kids being thrown into the first team understand the level of performance required of them going forward.
"Rangers can definitely rebuild," he said. "From what I have seen, the owners who have taken over have come across quite well. It is maybe a new start for the club.
"I think Ally McCoist and Lee McCulloch are vital to that. Can you imagine what it would be like if they weren't there?
"There would be nobody who understood the club and its traditions and knew the standards that are required. That would be horrible.
"Lee staying, in particular, is important for the club. He is a Rangers man through and through. He loves playing for them and is captain now. In many respects, it is good for him. Why would he want to leave?
"I think it is brilliant what he is doing, staying at the club and playing on even though they have dropped down to the Third Division, and I wish him all the success in the world. I really respect his actions."
Dailly continued: "It would have been fairly ghostly at the club if none of these guys, Ally or Lee, Kenny McDowall or Ian Durrant were still there. It gives people something to hang on to.
"You can't lose games at Rangers. That was something that really struck me when I joined. I had played for a long time down in England for Leicester, Blackburn Rovers and West Ham, but the mentality at the club was incredible.
"Guys like Lee know what is required, understands that every game the team plays must be won and won well, and will ensure that those around him, the young boys who are being brought into the team, do also.
"I know the club has had a few indifferent results, away from home especially, but that is to be expected given the number of youngsters they have been playing. I am sure Lee will keep driving them and they'll get it right."
Dailly enjoyed working under Walter Smith, his old Scotland boss, during his short stint at Rangers and won every domestic honour in Scotland under him.
But he was also impressed with the abilities of his understudies including Durrant, McCoist as well as McDowall, and feels that the Ibrox club is in safe hands with that trio still in place in the Third Division.
THE former Light Blues man said: "Coisty has become pivotal to the club. I think he has come across really well during the club's difficulties.
"Just think about what he has had to go through in his managerial career so far in such a short space of time.
"It is incredible. I am sure that, whatever he does in his managerial career in the future, will seem pretty easy in comparison after what he has had to endure on and off the park.
"I had played with Ally with Scotland before I moved to Rangers. But there were no problems being coached by him when he was assistant manager to Walter. He was just the same.
"By the time you are a senior player you are already talking to younger players in a certain kind of way. He had already done it, and he was older than me.
"We were team-mates, but I was still a young lad. He was brilliant with me."
He was also greatly impressed with McDowall, the former St Mirren striker who has worked on the backroom team at Rangers since 2007, during his 18 months as a player at the Govan club.
Dailly said: "Kenny's great. There is a knack to getting the best out of people when you are a coach. You don't necessarily have to rant and rave. He speaks a lot of common sense. He is like Walter in many respects."
Dailly, who hung up his boots after a distinguished and lengthy career in the summer, is now a qualified athletics coach and is also studying a sports science degree at Manchester Metropolitan University.
He added: "We knew of the financial problems when we were at Rangers and I did wonder how the club was going to get out of the situation. Hopefully, now things have come to a head, they can get back into the top flight.
"No doubt about it, there are a lot of good, talented people still at Rangers, both on the coaching and playing side, who can help take the club forward."