With the game at the Riverside heading for a stalemate, Karl Henry was penalised for handling Scott McDonald's cross in the box just two minutes from time.
Marvin Emnes converted the resulting spot-kick before McDonald added a second in stoppage time to ensure the three points.
"It was a bad decision," Solbakken said of the penalty award. "The ball was kicked in very hard and he turned but he couldn't get out of the way.
"For me the referee has to be 100% sure to give such a big decision and I don't think he could have been. I think he should have over-ruled the linesman. It was a very bad one.
"It was a big blow to us because I think we were the better team.
"After the first 20 minutes were played the better football, we created the better chances and we had the momentum. "