After a first half dominated by the Golden Boys, Yeovil snatched an opening goal in injury-time through a Byron Webster header.
New loan signing Ishmael Miller, one of three debutants, made it 2-0 with another header eight minutes after the restart and the salt was well and truly rubbed in the wounds during second-half injury time when Joe Edwards scored following a counter attack.
The loss made it six games without a win for Watford and four consecutive defeats at home, and Zola said: "Today was a game where we couldn't really (afford to) lose so we are certainly in a difficult moment but I believe in this group and in these players.
"I believe we can get out of it. We will have to work harder."
When asked if his job was at risk considering recent form, Zola replied: "There is no point asking questions that I can't answer.
"But I don't need the threat of being fired or sacked to push me to react or do more. There is no need for that."