Nathaniel Chalobah's volley had given the visitors the lead at Turf Moor, but Charlie Austin levelled from the penalty spot after Gibbs ruled that Dean Marney had been fouled.
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."