The Argentine, 27, created Neymar’s two goals on Saturday as Barca beat Athletic Bilbao 2-0 to top La Liga.
“Messi is a star. I am improving playing with him,” said Brazil’s Neymar, 22, who came off the substitutes’ bench at the Nou Camp.
“He does things in training that I have not even seen… on the Playstation,” said Enrique.
Barca were struggling to break down Bilbao until substitute Neymar struck in the 79th minute, running on to a threaded Messi pass and scoring with a low shot.
Four-time World Player of the Year Messi set up the Brazil forward for his second five minutes later, dribbling down the right and squaring for an unmarked Neymar to pick his spot in the same corner.
“Messi is the best not only because of his goals but also for his assists,” said Enrique. “It is a pleasure and a privilege to have him in the team.”
Messi struck twice in Barca’s 3-0 home win against Elche in their opening game of the campaign and set up Sandro Ramirez to score in their 1-0 success at Villarreal on their second outing.
Seeking to improve on last season’s second-placed finish to Atletico Madrid, Barcelona are the only team with a perfect record of three wins in three La Liga games.
“I am very happy with Saturday’s match, it went perfectly, with two goals,” said Neymar, who was inconsistent in his debut season in Spain in 2013-14.
“I returned from international duty feeling a bit tired, it was a long journey. I hope that this year is my year.”
Luis Enrique also hailed the unsung hero of his Barca side so far this season – his defence – as the club earned their third clean sheet in as many matches.
“Sergio Busquets’ tactical intelligence, how he interprets the pressure,” he added. “He’s a key player for us and the best in the world in his position.
“To be a team that wins titles you must have a good attack and a defensive phase, to be a complete team.
“Sometimes you can play too long and others you can have possession. Getting the right balance isn’t always easy.
“A team is formed to unite different personalities and profiles of players. I’m happy with what I have.
“I won’t explain why whoever plays to the players and I won’t do it here. We always hope to have the best version of each player.”