The Merseysiders won the League Cup and reached the FA Cup final last season with Kenny Dalglish in charge, but they have failed to replicate that success this term and currently occupy seventh place in the Premier League table.
When asked if the club was moving forward, Enrique told reporters: "In terms of football and for the future, I think so.
"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.
"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."
Enrique joined Liverpool from Newcastle United in summer 2011 for £7m.