Clayton Donaldson won the first of his two spot kicks on Saturday after a challenge by Frazer Wright.
And, on the Scottish FA's Whistleblower site, Dougal said that, after reviewing television evidence, it should not have been given as a foul.
Television pictures clearly showed that Wright played the ball firstHowever, the referee's admission does not affect the yellow card shown to the Kilmarnock defender during the Scottish Premier League game.
Dougal said: "I was approaching play from behind and saw Mr Wright slide tackle his opponent.
"From my angle, it appeared as if he had played through the opponent, thus fouling him, to win the ball and I was sure of my thoughts.
"However, after viewing the incident on TV, I can see that Mr Wright played the ball cleanly first just before there was contact with the attacker.
"People will question why the stand side assistant referee didn't get involved, but he could not see if there had been initial illegal contact.
"We were using radio communication equipment with immediate contact."
The penalty, scored by Donaldson on his way to a hat-trick, was awarded at a time when Hibs were 1-0 ahead.
"Making decisions is mainly down to angles and, on this occasion, while we were both in the recognised positions for this type of move, our angles were such that we were not best placed to see the incident as clearly as was shown on TV," added Dougal.