The Iranian Students News Agency reported on Monday that Shamkhani had made the accusation while visiting a university in Tehran.
Last Friday night, four people -- who later claimed to be followers of Iranian cleric Hossein Shirazi -- climbed up to the embassy’s balcony and removed an Iranian flag.
The four were quickly taken into custody by UK police.
Shirazi was detained in front of his house on March 5 in Qom city of Iran.
His detention has sparked protests in Iraq’s southern Karbala province.
Ayatollah Hossein Shiraz, was also arrested in February following a sermon he gave.
Originally an Iraqi national, Shirazi is known for his harsh criticisms of the Iranian Supreme Leader Ayatollah Ali Khamenei and the Tehran government.