Stephen Nicholson, 25, is accused of fatally stabbing the schoolgirl in the neck and upper body near a sports centre in Southampton last July.
Winchester Crown Court was told Nicholson was a lodger at the home Lucy shared with her mother Stacey White and stepfather Richard Elmes, who was his best friend.
When asked by prosecutor William Mousley QC if he acted appropriately with the teenager, Nicholson said swearing at her and “pushing her away from me was too much”.
He told the trial she was “vulnerable” and he did not kill her, adding: “We didn’t get along … at the same time I do not feel any child should be killed.”
Mr Mousley said to him: “Her wanting to be close to you, wanting to be next to you, wanting to be with you, that was the behaviour of a girl who had been having a sexual relationship with you?”
Nicholson replied: “There was no sexual relationship.”
Mr Mousley read a letter from Lucy found the day after she died, which said: “To Stephen, I have missed my period for almost two months. To be honest I think I am pregnant.”
The prosecutor asked him if he was concerned when Lucy “blackmailed” him the day before she was killed by asking for money and threatening to tell her mother she was pregnant.
Nicholson replied he was “not interested” and went on to say: “I have never slept with anyone underage so I know I am not a paedophile.”
The defendant is charged with murdering Lucy as well as three counts of rape against her when she was 12.
He also faces a charge of sexual activity with a child against Lucy on multiple occasions when she was 13.
Nicholson is also charged with sexual activity with a child in relation to a 14-year-old girl in 2012.
The defendant, of no fixed address, denies the charges and the trial continues.