Zola was disappointed with Gibbs' decision to award a 28th-minute penalty to Burnley after Dean Marney was fouled, allowing Charlie Austin to equalise.
Earlier, a well-struck volley from Nathaniel Chalobah gave the Hornets the lead but Zola was left to reflect on two dropped points in a 1-1 draw.
Zola said: "I was getting angry towards the referee, in fact a few of us were.
"I wasn't very pleased with the penalty, it was unclear and I'll have to see it again.
"I wasn't angry as such but I wasn't pleased that is for sure. Angry is too strong a word but I was disappointed.
"It is not going to be easy for anyone to get points here because Burnley are a tough side to play against.
"I would like to be in the play-off zone at the end of season. The table is short and we need to keep working and improving so I am not too concerned.
"We didn't create as many chances as we usually do and the passing wasn't fluid but that is to be addressed during the week."