Everton 2 Newcastle United 2
Substitute Victor Anichebe, whose earlier header had appeared to cross the line but was not given, thought he had won it three minutes from time but Demba Ba scored his second of the night even later.
Leighton Baines had put the hosts ahead in the 15th minute only for Ba to score with virtually his first touch after coming on at half-time.
Marouane Fellaini's effort was ruled out on a questionable offside decision before Anichebe's disallowed goal added to the controversy.
After the game, Moyes confirmed he had spoken to the match officials about the controversial decisions.
"There are two goals missed so I can't get them back but you hope that the linesman has a look and sees how he missed them," he said.
"I had a word and said 'You've missed two goals' and it does affect the outcome of the game but what can I do about it?
"I am sure the referee will have a look at them himself and see if he got it right or wrong - which we all know because we have seen it.
"Fellaini's goal was onside and if your job is to look along the line you hope the linesman sees if the ball crosses the line but we've seen many occasions where they don't get it right.
"I thought the offside goal was a goal from the touchline so I was surprised when it was ruled out.
"The other one you can't really tell but the reaction of the players was that they felt it was over and they are not usually far off the mark."
His opposite number Alan Pardew, who had to watch from the stands as he served the first game of a two-match touchline ban, admitted Everton had been hard done to.
"The one over the line was definitely in," he said.
"I have been saying all along that technology must come in and it has cost Everton a crucial goal tonight."
Pardew, who was missing goalkeeper Tim Krul and Fabricio Coloccini among others, was dismayed by their performance in the opening 45 minutes.
"The first half was as bad as I've seen us play under my tenure," he added.
"It was a team who lacked belief. I've never sent out a team to contain or defend.
"Demba's performance gave us belief but everyone stepped on to Everton and on the second-half showing we just about deserved a point.
"We were fortunate to come in at 1-0 down. The second half I thought we gave a really good account of ourselves with the team we had."
There was a concern after striker Nikica Jelavic was forced off before the interval but Moyes was hopeful it was not too serious.
"Jelavic has banged his knee against the post but I don't think it is too severe," he said.
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