Gemma Peters, 26, was left in agony following an horrific labour at Russells Hall hospital in Dudley, West Midlands.
The hospital has accepted liability for a string of errors that led to Brook's death, including the fact that midwives failed to act, despite the baby's head being stuck in the birth canal for 90 minutes.
When baby Brook was finally delivered, nurses placed her straight onto her mother's chest - but terrified Gemma had to beg nurses to help when she noticed her newborn wasn't breathing as the umbilical cord was wrapped around her neck.
Doctors then whisked the baby away to be resuscitated - but Brook suffered huge brain damage.
Gemma and her partner Liam Greenfield, 30, from Dudley, West Midlands, were advised that nothing more could be done and the decision was taken to switch off life support three days after she was born, on July 14, 2011.
Gemma said: "I had a healthy pregnancy and for everything to go so badly wrong at the end has been very difficult to cope with.
"I went through a long, painful labour and was totally exhausted. I was terrified but the midwife was totally disinterested in me.
"The midwives told me my baby's head was crowning and to keep pushing, but I did and nothing was happening.
"I had never had a baby before but I pushed for more than an hour and a half and I instinctively knew something wasn't right - I was really scared.
"This was my first labour and, like most first time mums, I put my complete trust in the midwives who I thought knew best.
"When we found out the extent of Brook's injuries, we were devastated.
"At one point the midwife admitted that she couldn't find the baby's heartbeat any more but just passed it off, saying it was probably because my pelvic bone was blocking the sound of the heartbeat.
"I had to trust her so I tried not to worry. I had been in labour for hours and was exhausted.
"She didn't try to reassure me, or tell me what to do - my mum, Debbie, who is a care support worker at the same hospital, and Liam, helped me get comfortable.
"They were the ones reminding me to breathe and telling me it would be OK, while the midwife just stood there.
"When I finally gave birth, I was so relieved I had finally managed to deliver my baby.
"I was so excited when they handed her over to me straight away, but when I looked at her I could tell straight away that she wasn't breathing. I felt sick, my emotions were all over the place.
"I could see the cord knotted around her neck - it looked like it had been strangling her. I started screaming: 'She's not breathing', and suddenly someone came and took her off me.
"All the midwives went with Brook, and I was left alone, terrified of what was happening.
"Liam went to try and find out what was going on, and my mum looked after me and helped clean me up, because there was no one else there to do it.
"When we found out the extent of Brook's injuries, we were devastated. Agreeing to have her life support switched off was the hardest thing I have ever done."
Gemma, who now has an eight-month-old daughter with partner Liam, added: "I am so angry about what happened.
This was my first labour and, like most first time mums, I put my complete trust in the midwives who I thought knew best. Their mistakes led to us being robbed of our beautiful baby girl and although the hospital has apologised, nothing can turn back the clock.
"If I could give advice to any other expectant mum, it would be to make sure the midwife regularly checks your baby's heartbeat during labour and insist on a second opinion if necessary because things can go wrong at the last minute."
Following legal action, the Dudley Group of Hospitals NHS Foundation Trust admitted full liability for the errors which led to Brook's death.
Jenna Harris from Irwin Mitchell's Birmingham office, who specialises in birth claims, said: "This is a tragic case and Gemma and Liam understandably remain completely devastated by the death of their first child.
"The trust has admitted that the care Gemma received from their midwives fell well short of acceptable standards.
"They agreed with our medical expert's view that, as the birth was taking longer than expected and attempts to listen to the baby's heart were unsuccessful, the midwives should have called for urgent medical help.
"Had they done so it would have become apparent that Brook was in distress, earlier delivery would have resulted and on balance Brook would have survived.
"Although the trust has now admitted liability they need to now reassure patients that the problems identified have been acted upon and that the midwives concerned have been retrained so that no other parents suffer such unnecessary tragedy."
Paula Clark, Chief Executive of the Dudley Group NHS Foundation Trust, said: "We would like to offer our most sincere condolences to Gemma Peters on the sad loss of her baby, Brook, at three days old.
"We have received a claim which is now in the hands of the Trust's legal team. Unfortunately we are unable to comment further."