It was the Uruguayan's first start at the Camp Nou since his summer move from Liverpool, but it did not end well for the forward as Joaquin Larrivey netted the only goal of the game to give Celta a shock victory.
"The other day against Real Madrid to return to playing was a bittersweet feeling, it was great to be back but we didn't get the result," Suarez told the club's official website.
"To make my debut in the Camp Nou in a competitive game was nice but the result is negative again. We created a lot of chances, but we didn't have luck on our side. They defended well and their goalkeeper was great.
"Football can be unjust at times, the opponent creates one chance in the whole game and scores and that hurts."
Suarez, who cost Barcelona £75m, is yet to score for the Catalan outfit in three appearances.