The FA said in a statement on Tuesday the Uruguayan international had accepted a charge of violent conduct but "has denied the FA's claim the standard punishment of three matches is clearly insufficient for this offence".
The incident in Sunday's 2-2 Premier League draw at Anfield was not seen by match officials and is being retrospectively reviewed.
"All of us who compete at a thousand revs and maximum adrenalin are prone to some mistakes," Lugano said on his personal website. "Luis is the most competitive of all. He made a mistake and said sorry.
"In the same way that a defender makes a mistake going for the attacker's leg instead of the ball or when coaches, referees, journalists or even directors make mistakes without the adrenalin of competition.
"The [Uruguay] squad support him because you see people's quality in everyday things. The people who work with him like, respect and protect him, as much in Uruguay as Holland or England. That's the most important thing in life."
The Uruguayan Football Association (AUF) is also defending Suarez from punishment by world football's ruling body FIFA for punching Chile defender Gonzalo Jara in a South American World Cup qualifier in Santiago last month.
