But a VAR check found a foul by Matt Garbett in the lead-up to the goal which ruled it out. Another VAR check in the second half saw substitute Kosta Barbarouses upgraded from a yellow card to a red for a reckless tackle.
UAE referee Mohammed Abdulla Hassan Mohamed was overawed and looked out of his depth as Costa Rica wasted time in the second half.
Although he has been a Fifa official since 2010, it was the biggest game of his career, given what was at stake.
The fourth official, along with the three men looking after VAR were all from Qatar.
Reid said he would have liked a more experienced referee in charge of the game.
"My general concern, I wish Fifa for a game like this would have given us someone more experienced. But that's the way it is. There were some decisions that just didn't go our way, unfortunately. But that's part of football and that's what happened today. It's just disappointing."
Despite the defeat Reid, who was part of the 2010 World Cup side that went undefeated in group play, was proud of the side's effort.
"I knew we were able to play up to this level because I've seen it so many times in training and sessions but to go out there and play so well on an evening we should have deserved more but … that's football."
