The British-drafted statement, agreed after Russia had blocked a virtually identical statement at the weekend, called for "immediate, safe and unhindered" access to Qusayr.
It warned that those who violate international law in any humanitarian operation "will be held accountable."
Syrian government and Lebanese Hizbullah fighters took Qusayr, a key town near the Lebanese border, on Wednesday after more than two weeks of bitter fighting.
It is the first time in several months that the 15-member council has agreed a statement on Syria that was not a routine condemnation of a terrorist attack. Russia and China have blocked three Western-proposed resolutions aiming to increase pressure on
Hereditary President-for-Life Bashir Pencilneckal-Assad
The Scourge of Hama...
's government over the conflict.
Britannia's U.N. ambassador Mark Lyall Grant, U.N. Security Council president for June, said the move was "significant".
"We were obviously disappointed that it didn't prove possible to agree a press statement at the weekend but we are pleased that it has been possible to achieve this humanitarian statement."
"I think it is significant and it's a sign that perhaps the Security Council is coming back together a little bit on the Syrian issue. But it is only a very small step and we will have to see what develops as a result of it."