In just 82 seconds, Masood killed four people and injured more than 50 before being shot dead by police on Wednesday.
Detectives have now revealed they fear it is possible "we will never understand why he did this".
Deputy Assistant Commissioner Neil Basu said: "We still believe that Masood acted alone on the day and there is no information or intelligence to suggest there are further attacks planned.
"Even if he acted alone in the preparation we need to establish with absolute clarity why he did these unspeakable acts to bring reassurance to Londoners, and to provide answers and closure for the families of those killed and the victims and survivors of this atrocity.
"We must all accept that there is a possibility we will never understand why he did this. That understanding may have died with him."
The development came as heroic MP Tobias Ellwood, who battled to save the life of PC Keith Palmer who was stabbed to death outside Parliament by Masood, spoke of his heartbreak that his efforts proved futile.
Mr Ellwood said in a statement: "I am heartbroken that I could not do more for Pc Keith Palmer who gave his life in holding the line against terrorism and defending democracy.
“I shall be writing to the family of Pc Palmer to offer my sincere condolences.
"It is right that despite the terrible events on Wednesday, Parliamentary business continued the next day as usual, the democratic machine was not interrupted and our way of life did not stop.
"I'm deeply humbled and overwhelmed by the messages of support, especially from the policing fraternity, which I now realise is as close knit as the military's in supporting its own.
"I played only a small part that day, doing what I was taught to do, and am honoured to have been invited to join the Privy Council afterwards.
"It is right that we concentrate our thoughts on the victims as we stand side by side to protect all that we hold dear, including our precious values and way of life which will always prevail."
Masood killed three others in his rampage, during which he mowed through pedestrians on Westminster Bridge.
After launching a knife attack on Pc Palmer, Masood was shot down by armed police. He later died.
Masood's victims on the bridge included US tourist Kurt Cochran and his wife Melissa, from Utah, who were on the last day of a trip celebrating their 25th wedding anniversary. Mr Cochran was killed and Mrs Cochran was badly injured.
Aysha Frade, who worked in administration at independent sixth-form school DLD College London, in Westminster, also died. She is believed to be a 43 year-old married mother of two.
Leslie Rhodes, a retired window cleaner from Clapham, south London, died from injuries sustained in the attack. He was described by neighbours as a "lovely man".