Enrique won the League Cup with Liverpool in his first season at the club under then boss Kenny Dalglish but the club haven’t experienced further victories during this campaign.
However the 27-year-old has defended the lack of silverware this season and insists the club have progressed, even if their results do not show it, and will continue to improve in the future.
"In terms of football and for the future, I think so," Enrique told reporters. "As the manager said from the start, it's difficult because he came to the club with another type of football that we're not really used to in England.
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"You can see how difficult it is to win a trophy. We won one last year and nothing this year, but in terms of the future we have made progress."
The former Newcastle United defender has fought to reclaim his favoured left-back position, ousting Glen Johnson, and insists he will strive to stay there as he continues to enjoy the new style of football implemented by Rodgers.
"I will try to stay there [at left-back]. I don't like to speak about myself but, for me, Glen is one of the best right-backs in the world," Enrique continued.
"He [Brendan Rodgers] wants the full-backs to try to be another attacking player. It's really good; I really enjoy this type of football.
"It's good because it's not just about defending and then attacking sometimes, he wants us to go all the time as another attacking player."
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