Stein was manager in 1967 when the Hoops became the first British club to win the European Cup and during a successful tenure also guided the Glasgow club to nine successive league titles.
It is 31 years to the day that one of the Celtic's greatest servants, while Scotland boss, died after World Cup qualifying game in Cardiff.
Rodgers mentioned the significance of the day - and the fact that it was five years since his father had passed away - to the players before the Hoops romp.
Moussa Dembele, who was only playing due to an injury to star striker Leigh Griffiths, grabbed the first Celtic league hat-trick against Rangers since Stevie Chalmers in 1966, with further goals from Scott Sinclair and substitute Stuart Armstrong.
Joe Garner's goal for Rangers proved to be a consolation for the Ibrox side who ended up with 10 men after debutant Philippe Senderos was sent off for picking up two yellow cards.
Rodgers, who confirmed that Griffiths is out for the Champions League game against Barcelona in midweek, while skipper Scott Brown will be monitored after picking up a knock, said: "It is ironic
My father is five years dead today so it is ironic that we scored five goals and obviously Jock Stein was 31 years today
"This is a guy who created a template of playing football here that to this day hopefully he looks down proud and sees a team with that mentality.
"Front foot, aggressive, no fear and when things go against you have that mentality to bounce back."
Rodgers, after his first Old Firm match, admitted the occasion was "everything I expected and more" and praised 20-year-old Dembele who has had to play second fiddle to Griffiths in recent weeks.
He said: "Moussa could play every week but I have to make the team work.
"Sometimes he will play, sometimes he won't.
"Leigh is a wonderful finisher but it wasn't his day today, it was Moussa's day and the rest of the guys.
"So, three great goals, a 20-year-old player, you can see he is a big talent and hopefully he has come to a club who can develop that talent."
It was a perfect day for former Fulham striker Dembele, who joined the Hoops in the summer.
He said: "To beat Rangers at home and for me to score my first hat-trick is unbelievable and I will remember it all my life."
Rangers boss Mark Warburton accepted the blame for his side's crushing defeat after going for broke at 3-1 down.
He threw on forwards Martyn Waghorn and Harry Forrester but the move backfired when he lost both his centre-halves, with Rob Kiernan limping off moments before Senderos' dismissal.
The former Brentford manager said: "We're obviously disappointed
We started the game saying don't allow them to come out hard and fast
The first 20 minutes were nip and tuck.
"We felt comfortable but goals change games
We were poor from the corner
They put the extra man up and we didn't pick him up.
"The second goal was a loose release, a poor decision.
"But then we got the goal and wanted to come out hard and fast in the second half
We did and for 15 minutes I thought we were good.
"Again, though, goals change games and from our point of view it was a poor one.
"The sending-off, I can't defend, it's a red card but we had a choice to make, do we go for damage limitation or do we look to try and get something out of the game.
"That was a choice I made, no-one else, put on Harry, put on Waggy, be positive and try to get a second goal.
"Apologies to the support because they were magnificent
But at 3-1 that was my call to try to get something from the game."
Gers have now slipped four points behind their rivals, who have a game in hand, after just five matches.
But Warburton is refusing to write off his side's title hopes already, insisting: "It's game five of a long season.
"We don't see a major gulf
We just got beat 5-1
Today they have the bragging rights and deserved to win today but there is no major gulf
We just need to work harder."
Source : PA
Source: PA