Suppose that due to more stringent environmental regulation it becomes more expensive for steel ...

The increase in the cost of production of steel will shift the supply curve to the left.  This effect alone on the market will influence the market price to rise while the market quantity will fall.  This is shown above by a movement from the original supply curve S0 to a new supply curve such as S1.  The decrease in demand will cause the demand curve to shift to the left.  This effect alone on the market will influence the market price and quantity of steel to fall.  Note that the supply and demand effects on price work in opposite directions.  If the supply effect dominates the demand effect, the equilibrium prices will rise.  This is exhibited by the decrease in demand to D1'.  On this demand curve, the net effect is for prices to rise from P0 to P1'.  On the other hand if the demand effect dominates, the equilibrium price will decline.  This is exhibited by the decrease in demand to D1''. 
On this demand curve, the net effect is for prices to fall from P0 to P1''.  As we don't know given the current information which effect dominates, we can't perfectly predict the change in price.  The change in equilibrium quantity is unambiguously decreased.