The Premier League side were eliminated by Besiktas on Thursday, suffering a 5-4 penalty shootout loss after the tie finished locked at 1-1.
The European exit may allow Liverpool to focus on securing a top-four league finish, while they are also in the FA Cup last eight.
Asked if the elimination was a blessing, Rodgers said it was too early to tell.
"We'll see at the end of the season if that is the case," he said.
"We have got the Champions League position that we want to fight for, a quarter-final of the FA Cup.
"Our objectives are still there to achieve and we will do everything we can to achieve them."
Rodgers was full of praise for a player who featured in central midfield in Turkey in Emre Can.
Can, 21, has featured mostly in a back three this season, but was given his opportunity in midfield against Besiktas.
Rodgers believes Can can develop into a key player at Liverpool.
"I thought he was outstanding in the middle," the Northern Irishman said.
"He is such a top class football player. His pace, his power, his ability to read the game and his ability to take the ball are all so impressive.
"He likes to play but he also like to play in that back three as well and drive forward. He gives us that confidence on the ball.
"He has played three or four positions for me and he is a top-class footballer."
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