Sunday's 1-1 draw at home to Newcastle left Brendan Rodgers' side 12th and six points adrift of Everton in fourth but Enrique says progress is being made.
"Of course, it's not a good position to be in the table," he said. "We want to be in the top four and I know that is difficult at the moment, as there are many teams above us.
"But, if we had beaten Newcastle, we would have been only four points behind the Champions League positions.
"It's not that far away. If we were to win three or four games in a row, we would be up there."
Liverpool are playing in a different fashion under Rodgers and, having returned to the side following an injury to Glen Johnson, Enrique is enjoying the change.
"With this manager, the style of play is different than we played before," he said. "We are all getting used to it and every game we are playing better. It's great to play like this and it will get us results.
"I use a lot more energy going forward now - against Newcastle I played many times like a striker - as this is the type of football the manager wants from his full-backs.
"Defensively I have less work now than before, I am more of an offensive player. Against Newcastle I was able to get forward a lot, like I did when I was playing in Spain."
So far Liverpool have scored just 13 league goals, five of those coming at Norwich, and forward Luis Suarez has scored seven of them.
Enrique said: "We need more people in the box. When myself, Glen and Andre (Wisdom) are playing we try to go forward and, if you do that, you have more chances and more players to score goals.
"I enjoy attacking more than defending. In games like this, where we are in control, I'm able to attack and try to get into the box.
"It's a dream to play with someone like Luis but we can't depend on one player. We need more players to score, as we can't always look to Luis."