Briefing the Council in a closed-door meeting, Mr Annan said he was particularly concerned about violence surging after UN monitors leave cities.
Activists said 70 people were killed on Monday, mostly in the city of Hama.
The UN wants to increase its monitors in Syria from a handful to 300.
Mr Annan said the overall situation was “entirely contrary to the will of the international community”.
He said that reported government firing on protesters in Hama, if confirmed, was “reprehensible and unacceptable”.
Earlier Mr Annan’s spokesman, Ahmed Fawzi, said in remarks broadcast on UN television that satellite imagery showed the Syrian government was failing to withdraw heavy weapons from urban centres.
He also said there were credible reports that people who met monitors were then approached and sometimes killed by security forces.
The UN says about 9,000 people have died since pro-democracy protests began in March 2011. In February, the Syrian government put the death toll at 3,838 – 2,493 civilians and 1,345 security forces personnel.
Source: BBC News