Suarez was given an excessively harsh 10 match ban this week for biting an opponent.
"Yes, I do understand, 100%," Rodgers said. "This is a guy who I see on a daily basis trying very hard. His two passions in life are his family and Liverpool Football Club. He throws his life into that.
"It is part of his make-up – you can't change that – but I genuinely think he is trying to adapt those traits he has grown up with as a kid to life and the culture here.
"Each time he makes a step forward we find ways to beat him with a stick and beat him down. I can understand if he felt like that [wanting to quit England] in a moment of reflection."