The game turned when a Scott McDonald cross was drilled into the box and hit Karl Henry on the arm two minutes from time. The linesman indicated to the spot and the referee gave the penalty which Marvin Emnes slammed home before McDonald sealed it deep in stoppage time.
"It was a bad decision," Solbakken said.
"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."
But Tony Mowbray insisted the officials had got the decision right.
"I'm not going to question the integrity of the officials, they call it honestly every game," said the Boro boss. "The boy leant into the ball and that's why the linesman called it how he did."
With both Cardiff and Crystal Palace dropping points the Boro boss admitted the win was of massive significance.
"It was a huge result for us," he said. "It wasn't the most fluid or polished we have played all season but that doesn't matter now.
"We can't play well every week but it wasn't exactly daylight robbery. We worked hard and kept going and I think we got our rewards."