"There are key moments which can affect games and the double penalty decision was one of those," said Black after the 3-1 defeat at Highfield Road.
"I'm quite sure Doyle was fouled as he made the box and I don't think there's any doubt about that.
"And as for the second one, our keeper's just put his arms up as Earnshaw's gone past him and away from goal but the referee's given that one.
"So after having played well in the opening period and got the goal we deserved, we very quickly found ourselves 3-1 down.
"We never really had a cutting edge though and but for those opening 15 minutes it was a poor performance from us overall."