Two defeats in four matches is not the start Liverpool would have wanted and has prompted several observers to question the club's title credentials.
But Lee says: "A lot has been made of what was said, but what Rafa said was that we all have to take responsibility.
"We all have to look at ourselves and make sure that when we have a bad result we analyse it and try and put it right.
"One thing about this football club is that we never get carried away - we are always looking at our own strengths and weaknesses to make sure we can improve."
He added: "You would have to say it has been a mixed start, results tell you that with two wins and two losses. But we've said on many occasions there are no easy games because the Premier League is the most difficult league in the world."