Dalglish was 17 years old when he broke into the Celtic first team just 18 months after McNeill had become the first British man to lift the European Cup following the club’s historic triumph over Inter Milan in Lisbon.
On a meagre wage at Parkhead, a car was beyond the future Scotland and Liverpool star’s means at that time so he would often take a lift from the Hoops captain to and from training.
It was those journeys which helped cement into Dalglish’s mind the standards required to reach the top.
And the lessons proved fruitful as he went on to replicate the success enjoyed by McNeill and the Lisbon Lions after making his move to Anfield, where he lifted the European Cup three times.
Paying tribute to McNeill, who died on Monday aged 79 following a battle with dementia, Dalglish said: “My condolences go out to Billy’s family and their loved ones. Marina and I are deeply saddened by the news as we have known the family for the best part of 50 years.
“I count myself as being extremely privileged to have been a team-mate of Billy’s and also his friend. He was an inspirational leader on the pitch but, just as importantly, he offered wise counsel off the pitch.
“This is a sad time but also a period to reflect and remember the happy memories. I’ll never forget how as a 17-year-old I got to train with Billy and other Lisbon Lions in 1968-69. I was in awe. They made every young player feel welcome.
“They never excluded you from anything, even to the point where Billy would pick me up on the south side of Glasgow and take me to training. I didn’t have a car so I relied on Billy and others such as Jim Craig and Bertie Auld to take me in.
“Billy looked after you or made sure you were looked after. That was his way. He set extremely high standards and others followed that exemplary leadership and kindness.
“Sharing the journeys in the car with Billy taught me how to handle success and be humble. To spend time with the Celtic captain was a wonderful education and stood me in good stead for my professional career and also as a person.”
Tributes to McNeill - who played a record 790 games for Celtic and twice managed the club as he racked up an incredible 31-trophy haul - have poured in from around the world since news of his death was revealed by his family on Tuesday.
Fans continue to flock to Celtic Park to lay wreaths and scarves at the former Scotland defender’s statue.
And Dalglish’s says his thoughts are now with McNeill’s wife Liz and their five children Susan, Paula, Libby, Carol and Martyn.
“Billy achieved amazing things in his career as a player and manager and he thoroughly deserved it all,” he added. “He was a wonderful person and a great family man.
“Liz has lost her husband, the children have lost their dad and the grandkids have their lost their grandfather. Right now, that overrides everything, including football.”