Scientific testing showed that blood found on the fridge in the apartment is 500,000 million times more likely to belong to Ms Millane than anyone else.
Her mother Gillian is additionally attending the trial.
Ms Ashcroft said she could tell Ms Millane was drunk because she was making typos and kept telling her how much she missed and loved her.
Jurors were shown security footage of the British woman, who had arrived a month before while on a round-the-world trip, visiting bars in Auckland with the accused, who can not be named for legal reasons.
The 27-year-old man's name has not been disclosed due to security concerns, has pleaded not guilty.
The defence claims the death, on either December 1 or December 2 previous year, the date of Ms Millane's 22nd birthday, was an accident during consensual sex.
Grace Millane died around her 22nd birthday in New Zealand.
Scientist Dianne Crenfeldt, from the Institute of Environmental Science and Analysis (ESR), informed the jury she had positioned two round possible blood stains between the accused's mattress and a wardrobe.More news: Celtics' Hayward fractures hand vs. Spurs
No buckets, however, were found in the apartment during the police search.
Evidence of a possible clean-up, she said, included circular marks, small drips of blood, footprints and smears.
She added: 'The shape of the probable blood staining and the presence of blood on the floor provided strong support that clean up of blood had occurred in this area'.
Ms Millane was shown to follow the defendant out of the lift at 9.41pm.
Millane had been dead for over a week before an autopsy was performed.
This morning the court heard luminol testing showed blood smearing on the carpet which indicated movement around the room when it was still wet.
The footprints clearly showed someone had walked in blood with their left foot, the scientist said, and "transferred ... blood around the room".
While there was no visible sign of blood on the top layer of the carpet, there was evidence of blood on the underside of the carpet, both sides of the underlay and the concrete floor below.More news: Iraqi PM concedes 'mistakes made' as protesters pushed back in Baghdad
Her parents had wept in court as they heard that earrings and a small metal tag inscribed with the word "freedom" were also found inside the suitcase.
It was the last time she was seen alive.
"I was also advised that the black sports bag, along with the bedding, had been taken to a dry cleaners where it had been cleaned".
Ms Crenfeldt said the cleaning of the carpet could have decomposed DNA evidence.
Yesterday, the court was shown CCTV footage detailing the pair's date the night she died.
She met the suspect on the dating app Tinder, and the pair were seen kissing and going to several bars in the city centre.
The backpacker was found to have 106mg of alcohol per 100ml of blood in her body, which is double the legal limit for drivers in New Zealand.
However, the crown alleges the accused murdered Millane and then attempted to hide his crime by burying her body, while the defence says she died while engaged in a consensual sex act, and the accused then made a number of poor decisions following her death, due to the stress of the event.More news: SoftBank CEO Masayoshi Son on WeWork Investment: 'Judgment Was Poor'
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