The Phobians came into the game on the back of a victory over rivals Asante Kotoko in the Super Clash and were hoping to make it two wins in succession but were undone by a Stephen Sarfo's first half goal.
"One of the main factors to our defeat in Berekum was officiating and I know if the Ghana Football Association watched the videos of this game, they would be very disappointed," said Nuttall.
“I would like the authorities to look at the videos again because it is very clear that the centre referee’s poor performance on the day affected the results of my side.
“I think we could have won the game against Berekum Chelsea, but some decisions which were taken by the referee affected us a lot in this game.
“I know it is a work in progress for Hearts of Oak and we are going to get better with time. We could have had a better result in this game, but it’s unfortunate for us. We want to improve and we would keep working towards that.
"The supporters should remain calm and keep urging the players on because things will be better very soon as expected," he added.
Hearts sit eight on the log with 12 points and will face Bechem United at home on Wednesday.