Zola was critical of David Sullivan's decision to write an open letter to supporters blasting the team's performance in Tuesday's 3-1 defeat to Wolves as "pathetic" and "appalling".
But Zola reported that both Sullivan and co-owner David Gold had been "supportive" after the game.
"The owners are behind us. They saw the team tried very hard today. They were supportive and that is a very good starting point," he said.
"The players will appreciate that. The players are feeling down and I am feeling down and to have that support is very good."