The Reds were beaten 5-4 in a penalty shootout at the Ataturk Stadium - the scene of their famous Champions League triumph over AC Milan on penalties back in 2005 - to be knocked out of the Europa League in the Round of 32.
Liverpool won the first leg 1-0 at Anfield last week but were defeated 1-0 by the Turkish side tonight after Tolgay Arslan beat Simon Mignolet in the 72nd minute which forced the contest into extra-time.
Rodgers felt his Liverpool team were unlucky to lose in the manner that they did but was now looking to focus on the Premier League and the FA Cup.
"We're very proud of the team, we put in so much effort on a very difficult pitch. It just wasn't to be. It went to penalty, and it's a lottery then," he said.
"It was something we figured it could work for us and in the main it worked for us.
"It doesn't add pressure. We had a disappointing campaign in the Champions League. Our objectives are still the same: to win a trophy and finish in the top four.
"He was brave to take a penalty. It's unfortunate, as he was brave enough to take one and it's a lottery, as I said."
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