Suarez stabbed the dagger in Madrid's heart with his goal in the 56th minute as Barcelona went on to win the match 2-1.
"[Suarez] played very well, like all the players," Enrique said after the match. "Very few players could score that goal, with his first touch and then a finish few can do. That is why we signed him, and we're very happy for him to be the decisive player.
"As a forward he needs goals, but we've always been happy with his attitude and displays. He is not just a typical centre-forward, he can join in the play with his teammates, read the moves and the play.
"He also has physical presence and character which are very useful for us. He has brought a lot to the team since his first day here."
Barcelona took the lead in the 19th minute when Jeremy Mathieu headed the ball into the goal following a magnificent free-kick from Lionel Messi.
Speaking about the goal, Enrique revealed that Barcelona had worked on the set-piece move in training prior to the match against Madrid.
"We work on everything – especially when it ends up in a goal," he said. "When you have a player like Messi who can deliver the ball with that pace and precision, and you have players to attack the ball like we do, it is very difficult to defend against."
Following Mathieu's goal, Madrid came roaring back in the 31st minute when Cristiano Ronaldo slotted the ball into the back of the net.
However, even though Barcelona had the last laugh, Enrique admitted that Madrid were on top for much of the match.
"Without any doubt, Madrid are reigning European champions, at a similar level to us," he said. "With players who can change a game, like we do. I congratulate my players, as they were able to suffer at times when Madrid had the ball.
"You must remember when you are playing against a team of this level, it will not always go exactly as you want. They were on top in some parts of the game. That gives even more merit to the victory. Both goalkeepers made good saves, maybe we had more chances, but these were two very good teams."