The Anfield outfit, who are also into the FA Cup quarter-finals following a victory over Crystal Palace at the weekend, face Besiktas in the Europa League's last 32, beginning with Thursday's first leg at home.
And Rodgers is confident of a strong run in Europe's secondary club competition, having been knocked out of the Champions League at the group stage.
"Now they'll recover and really look forward to the Europa League, because it's a competition we really want to do well in," he told the club's official website.
"It's a European competition, a very prestigious tournament and we are very focused on doing well in it.
"We have tough games with Besiktas, but we'll be ready for them. The players are young and hungry, and this is a group that can grow over the next couple of years.
"But we would like to get a trophy to signify that growth and the Europa League is a chance for that. The prize [of Champions League qualification for winning the Europa League] does make it more attractive. But we've a way to go before we can think of that."
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