Rodgers secured his first Premier League win as Reds boss on Saturday as Luis Suarez netted a hat-trick in a 5-2 success against Norwich City.
The Spanish defender believes that patience will be key as Rodgers aims to bring his style of play to Merseyside.
He told the Daily Mirror: "I hope that Rodgers gets the time he needs, because I think he is the best manager in England at the moment.
"I worked under five managers at Newcastle United and now two at Liverpool, so I know what I am talking about.
"The manager wants to bring a style of play like Barcelona's to the club, and that won't happen in just a few months.
"People say you cannot play the Barca way in England, but I disagree. But it will take time to adjust, I think we all understand that, because English football is so different."
Enrique has been frustrated by a knee injury in the early stages of the season, and was absent from the 18-man matchday squad for yesterday's trip to Carrow Road.