Janet Ajao said she had "shed many tears for the people caught up in this horrendous incident".
Masood killed three people when he drove a car into pedestrians last Wednesday. He then fatally stabbed a police officer before being shot dead.
Meanwhile, police say no evidence has been found of links between Masood and so-called Islamic State or al-Qaeda.
Mrs Ajao, from Trelech in Carmarthenshire, said: "I wish to make it absolutely clear, so there can be no doubt, I do not condone his actions nor support the beliefs he held that led to him committing this atrocity.
