Suarez was handed his official Barca debut at the weekend following a four-month ban for a biting incident at the 2014 World Cup.
However, Gudjohnsen believes that the Uruguay international would have been better coming off the bench in his team's 3-1 defeat.
"I thought he tried but we saw a player who hadn't played for a few months, a player with great qualities," he told Sky Sports News.
"He set up the first goal for Neymar and then set up a great chance for Lionel Messi to put Barca 2-0 up, but 'if' is a big word and if Messi had scored we'd have had a completely different game.
"All in all, it was probably the wrong decision to start Suarez in this match . What we also saw was Xavi [Hernandez] not at the top of his game and Andres Iniesta not finding his best level."
Suarez joined Barca from Liverpool in the summer.