The Reds have taken maximum points from only four of their 12 home matches so far this season, a record that the full-back is in no doubt needs to be improved as soon as possible.
The disappointment of defeat to Manchester United at the weekend was softened by losses to both Chelsea and Newcastle, with only Arsenal of those chasing fourth place, taking all three points from their weekend fixture.
The Reds remain unbeaten at Anfield in the league this season, but have drawn more than half of their home matches and with both Chelsea and Arsenal still to visit, Enrique believes turning draws into wins will prove vital.
"We lost [against United] but the truth is that we have to win more games at home," he said, speaking to the club's official website.
"We are still in the race to be in the Champions League next season.
"It's hard but Chelsea and Arsenal have lost many points too. Chelsea lost this weekend and we can't forget Newcastle.
"It's really important that we have to play these teams at home and we'll have another man - you play with 12 with our fans.
"It is hard to beat Manchester United at home but against teams like Blackburn and Swansea [both draws] at home we need to win the points.
"There are many games left and we have to beat many teams to try and be there.
"You never know in football - that's why everyone likes it. But we're still in the race."