Brendan Rodgers' squad made a sluggish start to the campaign under new management but finished in fine form, with just one defeat in their final 13 league games.
Despite ending the term strongly, they finished in seventh place, one position behind rivals Everton and 12 points away from fourth placed Arsenal.
Enrique believes that the side has been through a transitional period over the last year but are now starting to show their full potential.
Enrique said: "The top four has to be our target next season.
"It will be difficult as even with new managers the top clubs will spend a lot this summer to strengthen. But, to be honest, I don't think we have to
worry about the rest, we just have to worry about ourselves.
"The reason we weren't in the top four this season isn't because of any other team, it's because of our own mistakes. I think this is the best league in the world with so many teams fighting for those top places. Next season we hope we will be there."