Sergio Ramos's stoppage time equaliser salvaged a point for Real in a 1-1 draw in El Clasico on Saturday to maintain a six-point lead at the top of the table.
Barca have already dropped nine points at home this season in winning just three of their seven league fixtures at the Camp Nou.
"Right now there is a solid leader that have gone many games without slipping up," said Enrique.
"They have the resources and variety in their play to keep picking up points.
"The only chance we have to turn the situation around is to win every game we have left and to put pressure on them.
"We need to improve, above all, our numbers at home."
Ramos once again rode to Real's rescue with a key goal when they needed it most.
The Spanish international headed home a Luka Modric corner in eerily similar circumstances to lead Los Blancos to a 10th European Cup in 2014.
"It was a good ball in from Luka for a change," said Ramos jokingly. "I am delighted with the goal."
Ramos's powerful finish also stretches Real's unbeaten run in all competitions to 33 games.
"It is a reward for the good work that we have done since the start of the season," added Ramos.
"We can't go crazy, there is a long way to go but it is better to depend on ourselves."
Barca looked to have breathed new life into their title defence and the title race with a much improved second-half display following a tense first 45 minutes with few chances at either end.
Luis Suarez headed the hosts in front from Neymar's fine free-kick eight minutes after the break.
However, the normally lethal Neymar and Lionel Messi both fired off target with just Real 'keeper Keylor Navas to beat and the Catalans were left to pay a heavy price.
"The second-half was completely different," added Enrique.
"We closed the space between the lines, went ahead from a set-piece, we had the ball, tried to score the second and almost didn't even give away a chance against an opponent of that quality.
"We had two huge chances to kill the game with Leo and Ney, but that is football.
"It is a huge blow for all of us but we have only played 14 games in the league and there is a long way to go."