Solbakken flew into a rage when Brighton equalised to make it 2-2 in the 72nd minute, taking his frustrations out on the plastic dugout at Molineux.
The Norwegian said afterwards: “It was an instinctive reaction. I must have some hard power in me.”
The manager's mood darkened further when Brighton went in front through a disputed penalty in the 89th minute.
But 10-man Wolves - who had Karl Henry sent off - somehow salvaged a point with a late goal.
However, Solbakken cut a frustrated figure after the game, complaining about referee Scott Mathieson's decision to award the penalty.
"The ref made a big mistake," he said.
"When it is one minute left you should be 100 per cent sure that it is a penalty and it was far from a penalty.
"I think if we had lost 3-2 after the guts the guys showed in the second half it would have been hard to pick them up.
"I think the referee got the red card spot on, but when you see the replay for the penalty it is so far from a penalty."
The result leaves Wolves 15th in the 24-team Championship as they struggle to mount a credible promotion challenge.