Griffiths, who had earlier scored a penalty, was replaced by Scott Sinclair during the second half at Firhill.
The visitors won 5-0 and Rodgers said of Griffiths: "He is a brilliant boy.
"All strikers will be the same so he just needed a wee reminder that it is not about him, or any individual, this is about the culture of the team."
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With Moussa Dembele currently recovering from a hamstring injury, Griffiths has been leading the line for Celtic.
"For a minute he forgot himself," Rodgers said. "For a minute he thought about himself instead of the team.
"This is a team that is selfless. That's why I can change it about, the players know I trust them in their work.
"He was outstanding but he understood afterwards that I needed to protect him as the only fit striker at the moment. There is no drama."
Celtic manager Brendan Rodgers said Leigh Griffiths "forgot himself" after the striker appeared to question being taken off against Partick Thistle.