Moyes was aggrieved with Grant Holt's injury-time goal feeling the strike came after the allocated three minutes of stoppage time.
Everton were leading 1-0 up to the final six minutes with Kei Kamara's header and Holt's effort cancelling out Leon Osman's first-half opener.
Moyes admitted the result was tough to take after controlling the game for long periods as Everton's top-four hopes took a massive dent.
"It is tough to take we conceded two goals in the last five minutes or so," Moyes told Sky Sports.
"I think the second goal is well over the time, well over the three minutes allocated so that shouldn't have been given.
"We were in total control of the game and really we should have gone on to score a second goal and we didn't do that.
"I just think we should have gone on and won the game.
"We were winning 1-0, we were in complete control, we let the boy [Kamara] get a run on us for the goal for the header which got them back in the game, but it's an unjust scoreline, it really is."
Moyes refused to blame his defence for conceding the late goal, instead pointing the finger at their lack of killer instinct for not putting the game beyond Norwich.
"It can happen," he added. "We maybe didn't get up to the ball quick enough, I think maybe we were trying to see the game out.
"I thought when it was 1-0 we should have gone on and scored a second, we had plenty of play in the final third, but we didn't capitalise on it and I think that is what in the end cost us."
Taking your, admittedly wayward, goalscorer at 0-1 and defending like hell didn't help much either. Simply put it's asking for trouble. I agree with yozzer it's starting to feel like we're being held to ransom over a new deal with Moyes and you can have all the players saying 'we don't think about that kind of thing' but something has changed from the manner in which we started the season. The January 'Fer' debacle didn't help. Just like heads, two goals are better than one. Is there anyone with a passing interest in football that does not understand exactly what Grant Holt does? FFS, at the risk of sounding like a sad kopite - this was supposed to be our year. I still don't understand where you would rather be Mr Moyes, who do you think is coming in for you if you can't keep a team on track for a full season? No 'bigger' club than Everton is going to entertain a half season, mid table finish. Grrr. Well done Canaries.- kalavrim