Miller, primarily a forward, came in at left-back and lasted over an hour before making way for Emilio Izaguirre as Scott Sinclair's 16th-minute strike took the Hoops 14 points clear of Rangers at the top of the Ladbrokes Premiership.
Rodgers claimed to sees similar traits between Miller and England international Ryan Bertrand, whom he worked with in the youth set-up at Chelsea and who went on to play in the Champions League final with the Blues before moving to Southampton.
The Celtic manager said: "I was delighted for a young player who has just moved position. I thought he did very well and he wants to learn and develop.
"I did a similar thing with Ryan Bertrand when I was at Chelsea. We took him in from Gillingham to Chelsea and he came in as a left-winger and in the same team was Scott Sinclair, who was a striker.
"I moved Scotty wide and put Ryan to left-back and he went on to play with England and won the Champions League with Chelsea and is now at Southampton and he's an outstanding player.
"I see similar sort of traits in Calvin, where he can do that one position behind but he's only 18 so he needs time to learn that position and role but he's got some outstanding qualities and can offer the club something going forward."