On a hot and sunny afternoon in Lisbon's Estadio Nacional, Celtic secured their place in history to become the first British side to lift the European Cup.
Lennox said the Lisbon Lions were a close unit
Bobby Lennox was part of Celtic's Lisbon Lions side that came from behind to beat Inter Milan 2-1 on 25 May 1967.
Forty years on, Lennox says his team-mates were never in danger of taking success for granted.
"We were just a team going out to enjoy every game we were playing," Lennox told BBC Sport.
"At no point did we think we were going to the final that year. To be honest, it was only at the final whistle against Dukla Prague (in the semi-final) that we realised we were going all the way.
"We obviously took a lot of interest in the draw, but Jock Stein didn't have to keep our feet on the ground, because we were a young side and, for us, it was just a big adventure."
The Italians were the tall good-looking ones - with oil dripping off them
Celtic's triumph in Lisbon was all the more spectacular given the fact that the 11 first-team players hailed from within a 30-mile radius of Celtic Park.
Lennox, who scored 273 league goals in 571 appearances for Celtic, said the players enjoyed a fantastic team spirit that was fostered long before that famous night in Lisbon.
"We had been to America for five weeks the year before and we were happy in each other's company," he said.
"Wee Jimmy (Johnstone) was my best pal. We roomed together on away trips and could always be relied upon to start a wee sing-song."
Celtic captain Billy McNeill lifted the European Cup
Lennox said the sight of thousands of Celtic fans in Lisbon had relaxed the players before the game - that and a quick song.
"Standing in the tunnel, the Italians were the tall, good-looking ones, oil dripping off them," explained Lennox.
"We just started singing the Celtic song and the Italians looked round to one another like 'what's happening here?'"
Inter Milan, managed by Helenio Herrera, were a formidable defensive unit and overwhelming favourites for the game.
Stein, on the other hand, had fashioned a Celtic side that loved to attack and brought their full-backs, Jim Craig and Tommy Gemmell, forward at every opportunity.
"In our era, we played 4-2-4 and me and Jimmy would work back when we could," said Lennox.
Celtic went a goal down within 10 minutes when Sandro Mazzola scored from the spot.
But Lennox said the goal did not dent Celtic's confidence.
"During the game, we were never worried about getting back into it after going a goal behind," he recalled.
Jock Stein and his players paraded the European Cup at Celtic Park
"Jock said to us at half-time: 'you're doing well, the goal will come'. And we got the goals we needed in the second half.'
"We were a really fit side in those days and we could have played anybody and taken goals off them."
In the second half, goals from Gemmell and Stevie Chalmers gave Celtic the lead and they saw out the game to become European champions.
"It was just elation at the final whistle. I turned round and me and John Clark jumped on top of each other," said Lennox.
"But it was a terrible dressing-room - kind of mixed. There were too many people in there.
"So, it wasn't as though Jock stood up and said anything - it was bedlam."
Lennox said the highlight of the Lisbon victory was going back to Glasgow with the trophy and parading it in front of the fans at Celtic Park.
On the 40th anniversary, does Lennox believe Celtic can emulate the Lions and produce a Champions League-winning side?
"As a Celtic supporter, you can only hope. You live in hope," he said.
BBC One Scotland will screen Jock Stein: You're Immortal on Friday 25 May at 2305 BST