The Uruguay international, who joined Barca from Liverpool in the close season, was included in the starting lineup for the 'Clasico' at the Bernabeu and although he looked sharp and hungry he failed to open his account for the Catalan club as they fell 3-1 to their arch rivals.
Suarez provided the sweeping, cross-field pass to Neymar that led to the Brazil captain putting Barca ahead in the fourth minute and Lionel Messi should have scored from an excellent cross by the Uruguayan midway through the first half but was denied by Real goalkeeper Iker Casillas.
Suarez's participation in his first official game since he sunk his teeth into the shoulder of Italy defender Giorgio Chiellini at the 2014 World Cup finals in Brazil ended when he was replaced by Pedro in the second half.
"I am delighted to be able to play again," Suarez, whose FIFA ban expired on Friday, told reporters.
"It's a great relief and I am very happy to have put this period behind me," added the 27-year-old.
"The feeling is bittersweet because of the result but this team has picked itself up many times.
"It's very tough to play here (at the Bernabeu) but I came to contribute what I could.
"When we were pushing forward to chase the game we lost some control and they are very strong on the counter attack and killed off the game."
Barca top the La Liga standings on 22 points from nine matches, with Real a point behind in second.
(Editing by Toby Davis)
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