Suarez looked far from happy to be substituted with 12 minutes remaining of Sunday's 5-0 Barclays Premier League hammering of Swansea.
The Uruguayan had responded well to the frustration of squandering a number of chances in last Thursday's Europa League defeat at Zenit St Petersburg by scoring in an influential display.
But Rodgers wanted to give the 26-year-old some rest ahead of this week's return leg against Zenit at Anfield, when the Reds must overturn a 2-0 deficit to reach the last 16.
Rodgers said: "He just wants to help the team so much.
"If you look at the guy, coming back after the game at Zenit, when he could have been disappointed having had some chances - he is a real warrior of spirit, and he is a winner.
"He didn't want to come off. He wanted to stay on and get more goals.
"I've obviously got to think of the bigger picture.
"I wanted him to get a round of applause from the crowd because he deserved it, he worked his socks off.
"He is going to be very important for us tomorrow night. Giving him that little breather - at the time it is difficult for him to accept because he wanted to play - but he is a critical player for us."
Suarez is likely to carry the main burden of the attack against the Russians with Daniel Sturridge ineligible to play in the competition.
Fellow forward Fabio Borini is also ruled out after suffering a shoulder injury in the Swans clash at Anfield.
There were fears the Italian, who missed three months of the campaign after breaking a foot in October, could be out for the rest of the season and Rodgers has now confirmed he will sit out for at least six weeks.
Rodgers said: "The plan will probably be that by the weekend he will look to have an operation, then you are probably looking at six to eight weeks.
"It has been a difficult season for Fabio, coming into such a big club and then getting injured early, being out for three months, coming back, working hard and waiting for his moment, and then doing his shoulder.
"But he is a tough-minded young boy. He will get through his operation and then we will see how he recovers."
Defender Martin Skrtel also looks likely to miss the Zenit return having missed training on the eve of the game.
Rodgers said of the Slovakian: "He is being assessed. I think he will struggle.
"He had a little bit of a knock on it a few days ago and tried to train and made it worse.
"It is highly unlikely he will be involved."