There were grumblings of discontent around Celtic Park after goalkeeper Craig Gordon's failed attempt to play out from the back led to St Johnstone striker Steven MacLean opening the scoring just before half-time.
These grumblings were repeated once again in the second half when young left-back Kieran Tierney gave the ball away, which led Rodgers to signal to the supporters to calm down.
Substitute Callum McGregor scored a late equaliser for the hosts which allowed the Hoops to extend their unbeaten domestic run to 53 matches.
The Irish manager took responsibility for the visitors' goal, saying: "I always ask the players to play, to have the courage and the nerve to do that and if they make a mistake it is up to me.
"We had one example with Kieran, under pressure with no-one near him, probably felt as a young player that he had to smash it forward and we end up giving the ball away.
"I was signalling to stay calm. This is football. You have to stay calm when under pressure, not just the players but outside.
"Or you can play Scottish football. Just smash it up the pitch. It hasn't got you anywhere for 20-odd years It is understandable that the supporters want to see the ball in the box, but I've said since I came up here, the quicker it goes forward the quicker it comes back at you."