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 on Thursday. 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."