The Second Division side were leading 2-1 when Howard's 68th-minute shot crashed down off the bar and over the line.
Elleray, just yards away, waved play on. He then awarded a free-kick against Chesterfield for a foul by Andy Morris, and within two minutes Middlesbrough had equalised.
"I've seen the video and I accept the ball crossed the line," said Elleray, after watching a replay. "But I made the decision for another infringement before the shot. I could have made any of eight or 10 decisions so much was going on in there."
The Chesterfield players were convinced the ball had gone in, but their manager, John Duncan, chose not to dwell on what might have been on such a stirring day.
"Perhaps it was a goal but even if we had been 3-1 up it certainly wouldn't have been all over with the quality Middlesbrough have got," he said.
Duncan spoke of his pride in his side who cost little more than a 70th of the price of Bryan Robson's millionaires to assemble.
"People wondered if we'd make a game of it but we've definitely done that and made it a great Cup tie," he said. "It was a fantastic effort from the players. I cannot believe how proud I am of these lads. It was just a magnificent effort."
Elleray might have saved Boro, but that did not prevent Robson criticising the official.
"The referee did a great job at evening the sides up," he said, referring to the 37th- minute dismissal of the defender, Vladimir Kinder.
"Kinder's first booking was harsh and for the second he couldn't get the card out of his pocket quickly enough. They made it difficult, but the referee made it even more difficult."
Chesterfield's extra-time match-saver, Jamie Hewitt, admitted the first FA Cup goal of his career was something of a blur. "It was a great ball in from Chris Beaumont and when I saw it bounce over a couple of players I just threw my head at it," the 28-year-old midfielder said.
Boro's Juninho could not believe the result. "I think we all thought the game was finished at 3-2," he said.