Northern Irishman Allen, 31, led 5-2 before the four-time champion fought back to win.
"It's my own fault. I don't prepare properly for these tournaments," world number 11 Allen.
"I don't practise at 10 o'clock in the morning. I didn't get started until 12 o'clock today."
The Northern Irishman led 5-3 after hitting three century breaks in a brilliant first session on Friday only for Higgins to dominate Saturday's morning session as he moved 9-7 up.
Allen won the first frame of the final session to reduce the lead to the minimum but suffered a kick while on a break of 58 in the next and after Higgins pinched that frame, the Northern Irishman was largely frozen out for the remainder of the contest.
"I think 13-9 wasn't really a fair reflection on the match. I felt like I really played well in spells but a couple of things went against me," added the Antrim man.
"John played really well himself. Take nothing away from him. He closed out the match the way you would expect John Higgins to do."
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However, Allen felt the match slipped away from him in Saturday's morning session as Higgins took six of the eight frames.
"Twelve o'clock is normally the time when I'm getting up and lazing about the house," added Allen, who has won three ranking tournaments in his 12-year professional career.
"You need to prepare in all facets. Not just working on the table but working on the table at the right times. I just wasn't prepared for a 10 o'clock match."
However, when asked whether he will address the morning session issue in the future, Allen replied:"Probably not."
Allen added that he is attempting to lose weight in order to boost his ability to perform in the major tournaments.
"I've got to keep working hard and lose a bit of weight. I've lost a stone and half since the Masters. There's maybe another seven [stone] to go. I'll just keep working hard."
The Northern Irishman revealed that his hopes of working again with his former coach Terry Griffiths had been dashed.
"Myself and Terry thought we were getting back together. He's said 'no'. That's a hard one for me because we had a very close relationship."
Mark Allen blamed his failure to prepare for morning play for his 13-9 second-round defeat by John Higgins at the World Championship.