The Anfield manager feels the club has been shown a lack of respect by the striker, and insisted that nobody is bigger than the club
The striker remains determined to leave the club this summer for a side playing in the Champions League, with the Urugay international claiming an agreement with the Reds that would allow him to depart for a bid in excess of 40 million pounds.
But Liverpool is standing firm in its valuation of the player, and Rodgers has been left disappointed by Suarez's comments to the media.
"My conversations with players will always remain private," he told reporters after a 4-1 win over Valarenga. "I'll never disclose any conversation between a player and I.
"In terms of the remarks that were made, this is a football club that has always worked a certain way. The Liverpool way is all about a club with ambition, a club that strives to be the very best, a club that is about commitment. That means that everyone is committed to the cause of fighting for the shirt.
"It's also about dignity and being dignified in how you speak about the club, on and off the field, and it's about unity.
"Those are the four values that run through my mind when I think about Liverpool. Those are the values we will always retain. If anyone steps outside of that standard, I will deal with it. That's something that we'll do.
"It means that we have a standard at Liverpool that I will fight for my life to retain. There will never be any player or person bigger than the club."
Rodgers also indicated he felt the club had not been shown respect by Suarez, despite giving him its complete backing in several controversial incidents in the past.
"Professionally, Luis Suarez has given me everything since I came into the football club, but there is obviously a way in which you have to speak," he continued. "This is a club that has offered Luis Suarez the utmost respect since the day he walked through the door.
"That's something that over the course of the coming weeks you need to have when you work for Liverpool football club. You've got supporters and players that have given Luis Suarez absolutely everything - they backed him to the hilt.
"Even at the weekend, when we had Steven Gerrard's testimonial game, the supporters raised the roof for him. That's something that I will always fight to retain at the football club, because that is what Liverpool is about - respect, humility and real dignity."