The Anfield outfit edged into the fifth round of the FA Cup with a 2-0 win at Championship side Bournemouth on Saturday, and host local rivals Everton in the Premier League next week.
But Rodgers was not tempted to field a weakened team at Dean Court.
"We have a very thin squad, and along with that we've got a number of injuries, but the tradition of the FA Cup for Liverpool is huge," he said.
"We want to pay respect to the competition because we want to get to the final and win it if we can.
"The players have had enough recovery time and will recover well for Everton. They have everything there to recover.
"We go into Tuesday's game on the back of a good win against a good Championship side."
And the Northern Irishman was full of praise for Bournemouth and their manager Eddie Howe.
"Bournemouth are a very good side and we give credit to them first of all," he continued. "They have a great idea when it comes to playing the game. Eddie is similar to myself in terms of his philosophy.
"They were excellent, we didn't work hard enough in the first half, but once we re-organised at half-time we were much better."
Martin Skrtel required treatment for a clash of heads in the second half, but Rodgers reassured fans that he would not face a spell on the sidelines.
"He had staples in his head, so he might need to grow some hair now," he added. "He'll be fine."
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