The Scot was riled when played was not halted with Steven Pienaar stricken in the build-up to Danny Welbeck's goal which put the hosts 2-1 up shortly after the interval.
Earlier in the match, in a similar situation, Jones had brought play back when Jonny Evans was down injured and the visitors were on the attack.
Although the Toffees fought back from being two goals down in the final 15 minutes to cap off an incredible match, Moyes launched a blistering attack on the official.
He told Sky Sports: “I thought it [the refereeing] was rubbish. He stopped play for Jonny Evans.
“The referees can do what they want, can’t they? They really can. They can make their own mind up, make their own rules up. And I thought he made his own rules up today.
“Not to do the same on their goal - I don’t know whether it was their second or third goal - when Steven Pienaar’s down, you’d have thought then if he was being consistent that he’d maybe even it up, and say ‘Oh, the player’s down I’ll do that.’
“He never did it and they scored from it. I’ve got to say I think the referee was poor today.”
Although the score was level at half-time, goals from Welbeck, Wayne Rooney and Nani looked to have sealed a win for United.
However, Everton fought back magnificently and goals from Marouane Fellaini, Nikica Jelavic and Pienaar in the second-half earned them a point at Old Trafford.
"We always thought we could win,” Moyes revealed. “We felt as though we’d been a bit hard done by lately so the players didn’t half put on a show.
“Incredibly. I don’t think that at any time we deserved to be two goals down. We kept going. We knew it was going to be a bit of a gung-ho game. We decided we were going to make sure we got at them, try to make chances.
“So that was always going to happen when you come here. The finishing and the goals we scored were very good, but Manchester United scored some very good goals as well.”
Moyes defended his dismal record at Old Trafford and admitted his relief that the players bounced back from the FA Cup semi-final loss to Liverpool last weekend.
“I don’t think I’ve ever gone into any game and sat, I can honestly say that,” he said.
“I’ve only ever gone into any game to try and win it. But the emphasis was big here today to try and make sure we came here and got a result, because at the moment we’re down.
“We lost a big game last week and today was a chance to play another big game and to stop people from thinking our season’s over.”