Alistair was found at his Burnley home in August and pronounced dead shortly after being taken to hospital.
At the time, a representative for Jessica praised Alistair being a “really good father” and the TV personality has now shared a lengthier post on Instagram.
“The past three weeks have been incredibly upsetting, challenging and full of sadness,” she writes. “I want to thank the special souls that have brought light where there was darkness, helped my children to smile when there were only tears and helped them believe there is life after death.
“The strength and support from those closest to myself and my children has given me faith that they will lead as happy as can be and normal lives and that the hard choices I’ve had to make have been the right decisions.
“I feel truly saddened about what has happened as there was so much to live for.”
Jessica and Alistair had three daughters together before splitting in 2013 after he pleaded guilty to money laundering, though remained close for their children.
Jessica is best-known for her time on Alan Sugar’s programme, and she went on to take part in the ‘All Stars And New Stars’ edition of ‘Celebrity Big Brother’ in January - just one month after her stint on ‘The Apprentice’ ended.