The Reds finished 2012-13 in seventh place, 12 points behind Arsenal in fourth, but the Spaniard believes they have developed under manager Brendan Rodgers and will continue to do so over pre-season.
"The top four has to be our target next season," Enrique remarked to the Liverpool Echo.
"It will be difficult as, even with new managers, the top clubs will spend a lot this summer to strengthen but I don't think we have to worry about the rest, we just have to worry about ourselves.
|2/1||Liverpool are 2/1 with Bet365 to finish in the Premier League top four in 2013-14
"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.
"In terms of where we are in the league, it has not been a great season for us. Liverpool cannot be there - they have to be much higher for sure. You can see there are 12 points' difference between us and the top four but, in terms of being a football team, we have moved forward.
"We had some problems earlier in the season when we lost many points and now we regret that. We wanted to do well from the start but it was a different type of football with a new manager and a new type of training."
Some of the Liverpool squad have had trouble adapting to Rodgers’s passing style, Enrique explained, though his previous experience in La Liga had prepared him personally.
"I was one of those players who had played this style before when I was in Spain but a lot of players were not used to it," he added.
"Brendan wants us to play good football and I think every player is really happy with this way of working. Of course it takes time but since January we have done really well. Come next season we will be more used to this style and the system and we'll work better together."