"The process of identifying the victims is continuing and I'd like to stress that their nationalities are not confirmed at this stage," Xinhua news agency quoted Patel as saying during a Parliament briefing on Monday.
"I would also like to remind colleagues that this is going to be a long and meticulous investigation," she added.
Patel told Parliament that the "tragic events" in Essex last week showed "there is much, much more to do".
"We must be ruthless in our response," she said, adding that work was underway to coordinate an international response to the "appalling" incident.
Earlier Monday, Maurice Robinson, the 25-year-old lorry driver charged with manslaughter, appeared in court for the first time via video link.
He is thought to be part of a "global ring" of people smugglers, the Chelmsford Magistrates' Court heard.
A couple from Warrington who were arrested in Cheshire on october 25 have been released on bail until November 11, while a 46-year-old man from Northern Ireland who was arrested at Stansted Airport has been bailed until November 13, police said.
The police said all of the 39 people found in the lorry have been moved to a hospital for fatality victim identification.
Initially, police said the victims were Chinese, but a number of Vietnamese families have described how they fear their loved ones are among the dead.
DNA tests are being carried out in Vietnam to help to identify the dead.
The trailer arrived in Purfleet on the River Thames from Zeebrugge at 12.30 a.m. on October 23.
The lorry and trailer left the port at Purfleet shortly after 1.05 a.m. the same day. Ambulance staff discovered the bodies in the container at Waterglade Industrial Park in Grays at about 1.30 a.m.
( With inputs from IANS )