Mr Sheffield confirmed that he had awarded a second-half penalty and sent off Rams defender Richard Jackson for a professional foul in the 58th minute.
Jackson, who was making his 100th appearance for the club, was adjudged to have tripped James Chambers before Marlon King struck the post from the spot.
But the Derby contingent were really up in arms when Mr Sheffield raised his flag and then lowered it as Clarke Carlisle headed an 88th minute winner from Anthony McNamee's free-kick.
The free-kick that was awarded by referee Clive Penton for a foul by Seth Johnson on Lloyd Doyley, was also hotly disputed and the officials left the field to a chorus of abuse.
The day had started well for Derby whose passing was crisp in the opening stages and led to the opening goal in the fourth minute.
Grzegorz Rasiak crossed from the left, Jeff Kenna whipped the ball back into the danger and Adam Bolder thumped a first-time shot past the helpless Ben Foster from eight yards.
It took Watford some time to get into gear but, as the first half wore on, they began to make inroads into the Derby half.
Their best chance came on the stroke of half-time when Ashley Young's cross found Anthony McNamee unmarked at the post but he let himself down with a poor first touch and his delayed shot was blocked by Andrew Davies.
The visitors remained on top at the start of the second half and almost equalised in the 57th minute.
Young clipped a clever effort over Lee Camp from Anthony McNamee's cross and Michael Johnson raced back to clear off the line.
But the game really sparked into life when Jackson was red carded for what was deemed as a professional foul. King's miss from the spot lifted the home crowd but there was not reprise for Derby when Watford finally drew level in the 67th minute.
McNamee's cross from the right was held up well by King and he set up the unmarked Matthew Spring who was able to pick his spot in the top corner of the net from 12 yards. Camp then saved well from man-of-the-match McNamee but could do nothing as Carlisle rose to head in the decider.